It is hard to blame the narrator ("Brother") completely because he is just a kid himself. He openly admits his responsibility in tormenting Doodle and pushing him too far, though, so the narrator is largely to blame.

Brother says Doodle was "a disappointment" from the beginning. Brother wanted a more physically able companion. As a result, he resents Doodle. Brother torments Doodle by showing him the casket that was meant for him.

Brother teaching Doodle to walk seems like a generous gesture to his parents, but Brother reveals he only taught Doodle to walk out of shame.

They did not know that I did it for myself, that pride, whose slave I was, spoke to me louder than all their voices, and that Doodle walked only because I was ashamed of having a crippled brother.

At the end of the story, when Doodle has "failed," Brother leaves him, literally and symbolically. Brother runs away faster and faster, knowing Doodle will push himself but inevitably be unable to keep up. As Brother runs away, he feels a "streak of cruelty." He runs faster and pushes Doodle to run himself ragged. He puts Doodle through physical and emotional strain and this becomes too much for Doodle's body to handle.

Despite his love for Doodle, the brother is responsible for the death of the fragile boy.

It is significant that Hurst alluded to World War I in his setting of "the summer of 1918" as a backdrop for the scenes of the death of the scarlet ibis and that of Doodle. One textbook editor has observed that Hurst wants readers of "The Scarlet Ibis" to consider

...how the war raging among brothers in Europe is related to the conflict between Doodle and his brother. [Elements of Literature. Holt, Rinehart and Winston. 2008.] 

In the final lines of the story, the brother/narrator states,

I lay there crying, sheltering my fallen scarlet ibis from the heresy [meaning mockery here] of rain.

On the day that Doodle dies, the brother wants to blame the rain for the ending of his and Doodle's practice session and their need to hurry to get home. However, he admits that he was angry about Doodle's failure to succeed at "keeping up with the other boys." Knowing that Doodle is weak and after Doodle's "being too tired to swim," the brother still makes Doodle row back to shore. Not only must Doodle row, but he must row against the tide. Then, even though Doodle has been greatly strained, the brother runs ahead of him, forcing Doodle to try to keep up. When the brother stops to rest, he admits his cruelty,

I hadn't run too far before I became tired, and the flood of childish spite evanesced as well. 

It is only after this "evanescence" of his spite that the brother comes to his senses and he stops and waits for Doodle. While he has not meant to kill Doodle, the brother has acted selfishly all along. Also, having admitted previously to a "streak of cruelty," he has tried to force Doodle to become normal despite knowing that the small boy is frail. Even at the end of the narrative, the brother wants to blame "the heresy of the rain" as the reason for Doodle's death because this is why they hurried. But he is the one who has taxed Doodle's heart all along.

Despite the narrator's guilt over the situation, he is not to blame for his brother's death. He may have treated him with indifference and occasional malice, both of which are displayed by his words and actions in the story, but in the end, those words and actions were not the primary cause of Doodle's death.

We as readers know that his condition is what eventually led to his certain death, and that from the very beginning, Doodle was supposed to have died many times before. The fact that he had lasted as long as he had was a fact of sheer amazement.

In the end, the narrator cannot be held responsible for Doodle's death, but we can continue to hold him accountable for his harsh words and behaviors toward his now-deceased brother.

Now, of course, this is an opinion question, so the answer is up to you, as well as the evidence to support that answer.

In my opinion, however, the narrator is not at all responsible for Doodle's death.  Although, of course, he feels terribly to blame.

Doodle was destined to die.  To use this course of reasoning, you really have to argue that fate has a huge role in this story.  This is evident in the scarlet ibis's presence, which was a foreshadowing of what was to come.  Doodle was represented by this brilliant bird, and the bird died.  Doodle was supposed to die.

The narrator was only 13.  He was cruel, it's true, but he was also only 13.  He was acting how most boys his age do when confronted with something uncomfortable, like a disabled brother.  He was jealous of the attention Doodle got, and he was embarrassed by Doodle's difference.  He was probably also disappointed that he didn't have a brother who could run, wrestle, and play with him as he'd probably originally hoped.  There was a lot of emotion flooding through the narrator.  There is really no way he could have known that Doodle was hurt as badly as he was.  Plus, Doodle sustained a head injury and died so quickly that he would have died even if the narrator had run back sooner to help him.

And regardless of the narrator's motives for helping Doodle to walk, he did improve Doodle's quality of life for a short while, regardless of how frustrated Doodle sometimes got.

Is the narrator in some way responsible for Doodle's death in "The Scarlet Ibis"? Is his emotion at very end sorrow, guilt, or something else?

The narrator of "The Scarlet Ibis" is telling the story from many years after the events took place. The retelling then is colored by years of consideration, and guilt is definitely apparent as the narrator gives the details of his life with Doodle. At one point early in the story the narrator says,

There is within me (and with sadness I have watched it in others) a knot of cruelty borne by the stream of love, much as our blood sometimes bears the seed of our destruction, and at times I was mean to Doodle. 

In James Hurst's story "The Scarlet Ibis," to what extent can the narrator be held responsible for Doodle's death? Were his intentions cruel?

James Hurst’s short story “The Scarlet Ibis” is the sad tale of a boy and his brother Doodle. Doodle is disabled from birth and not expected to survive. However, he is able to exceed expectations; not only does he survive, but he also learns to talk and walk and in many ways live the life of a normal child.

To assess the narrator's actions, we need to first look at a few important lines from the story.

I wanted more than anything else someone to race to Horsehead Landing, someone to box with, and someone to perch with in the top fork of the great pine behind the barn . . . . I wanted a brother.

But Doodle cannot be this kind of brother—he is not capable of this kind of physical activity.

As Doodle grows the narrator, as his older brother, is given the responsibility of pulling him along with him in a go-cart their father made. Typically, as an older sibling, the narrator isn’t happy about it:

He was a burden in many ways.

The narrator also knows that Doodle could not be treated like ordinary boys:

The doctor had said that he mustn’t get too excited, too hot, too cold, or too tired and that he must always be treated gently.

But the narrator resents this and intentionally pulls him too quickly sometimes, causing him to fall out of the cart. Doodle, however, is loyal and never tells on him. Eventually the narrator comes to a realization:

Finally, I could see I was licked. Doodle was my brother, and he was going to cling to me forever, no matter what I did . . .

The story could have ended here and we could still consider it a complete, and even happy, tale. But life usually doesn’t work like that—we don’t get to divide our time into segments that allow for ideal endings. Events keep coming and our lives develop continuously. Unfortunately for Doodle and his brother the story ends with Doodle’s death.

When they decide that Doodle needs to work on becoming as physically adept as other boys before starting school, Doodle proves incapable of keeping up with his brother, who leaves him behind in a thunderstorm. The narrator’s own words here are:

The knowledge that Doodle’s and my plans had come to naught was bitter, and that streak of cruelty within me awakened. I ran as fast as I could, leaving him far behind with a wall of rain dividing us.

Can the narrator be held responsible for his death? Yes, I think so. We have seen that he knew that Doodle had to be treated carefully, but his own ambition for Doodle’s development overcame him, and he pushed Doodle too far. Doodle's death would not have happened otherwise. 

Are the narrator’s intentions cruel? This is an interesting question because the narrator himself admits to being cruel. However, we cannot always trust a first-person narrator. Just like a person verbally telling us a story about their lives, we can disagree with their statements, particularly their judgments. I personally don’t think the narrator was behaving out of cruelty. He was certainly not being as sympathetic as he should have been toward his brother, and he selfishly wanted him to change because he wanted a brother who was physically normal, but he was not trying to be cruel. In my opinion, at the end of the story he runs away from Doodle out of frustration, not out of cruelty.

In the James Hurst short story "The Scarlet Ibis," is the narrator responsible for Doodle's death?

Knowing that his brother's heart is weak, the narrator is, indeed, responsible for the death of his brother in forcing Doodle to run after him in the storm.

In her critical essay on "The Scarlet Ibis," Claire Robinson points to the dualities in life, the spiritual and the physical. Doodle has a spiritual awareness of the beauties of life while Brother focuses on walking, rowing, and running--all physical activities. Because these physical skills are so noticeable, he is ashamed of Doodle for not being able to perform them, ignoring the talents of Doodle and the gifts that he can provide others. Commenting on Brother's expression of "the heresy of rain," as he holds his dead brother in his arms, Robinson writes,

But it was Brother's own shame that killed Doodle, and the true heresy seems to be the fear of difference, the fear of dualities, the fear of accepting contrasting aspects. [Enotes]

At the beginning of Hurst's story, Brother describes his environment that is now barren in the absence of Doodle: the flower garden is "stained with rotting brown magnolia petals," and there are weeds growing. If an oriole sings in the elm tree, "its song seems to die up in the leaves." This description is clearly an admission of the beauty that has been lost with the death of his "scarlet ibis," Doodle. 

Furthermore, brother himself admits that he has born in his heart "a knot of cruelty" and he was "mean to Doodle" because his pride caused him to try to force Doodle to be normal rather than recognizing the special gifts that his sensitive brother possessed.

In the James Hurst short story "The Scarlet Ibis," is the narrator responsible for Doodle's death?

In the James Hurst short story "The Scarlet Ibis" the narrator is responsible for Doodle's death. Throughout the story, the narrator tells us of the displeasure and of the embarrassment caused by his brother.  The actions that the narrator takes in teaching Doodle how to walk, even when no one thought he would ever walk, are selfishly motivated as he admits through his tears that, "I did it just for myself, that Doodle walked only because I was ashamed of having a crippled brother." Success was achieved, but at what price?

The narrator kept pushing Doodle to achieve more and more challenging goals, and Doodle's physical limitations were disregarded since the narrator "...began to believe in my [his own] infallibility."

Perhaps the key to the narrator's culpability lies in his assessment of Doodle when he says, "Now he [Doodle], too, believed in me." Clearly, throughout the story, Doodle looks up to and idolizes his brother. He will do whatever he has to in order to earn the narrator's approval. Consequently, when the boys are caught out in the storm, and the narrator begins to run home, it is not surprising that Doodle will attempt to keep up with his big brother. So Doodle does, and he runs and runs until his heart gives out.

Enotes has some great resources at the following link.

http://www.enotes.com/scarlet-ibis