"The Ransom of Red Chief" is told from the first person point of view. The story's narrator is Sam, one of the hapless kidnappers who holds little Johnny Dorset for ransom. The use of the first person viewpoint is important because it allows us to gain some degree of sympathy for the criminals' plight, something we wouldn't ordinarily feel. If O. Henry had used a third person omniscient point of view instead, then we may well have felt much less sympathetic toward the kidnappers, believing that they got what they deserved.

It should also be noted that O. Henry himself served time in prison for embezzlement. This may account for the sympathetic portrayal of criminals here as elsewhere in his short stories, most notably the character of Jimmy Valentine in "A Retrieved Reformation."

The point of view in this story is first person.  The story is narrated by one of the kidnappers, Sam.  The story is told completely from his point of view.  He only knows what he sees and hears and thinks.  He has no special access to the thoughts of the other people in the story.

We know that this story is told in the first person because the narrator constantly refers to himself as "I."  He only tells us what he sees, and the narrative shows his own conceptions and ideas as to what is going on in the story.  Because of this, we only understand the other characters through the lens of Sam's own perceptions.