How does Anita Desai depict a child's disappointment in "Games at Twilight"?

I believe that the child you are referring to in your question is Ravi. He spends most of the story hiding in a shed from Raghu, because the kids are playing hide and seek. The entire time Ravi is hiding, he is envisioning what his victory will feel and look like. Ravi stays hidden for so long that all of the kids forget about him completely. By the time he runs to the den to claim victory, all of the other kids have moved on to many other games. The kids and the parents all tell Ravi to stop acting so foolish and join in the new game if he wants to play.

Of course Ravi is supremely disappointed that nobody is willing to recognize his victory. The description of his disappointment is contained within the last paragraph.  

But he had been forgotten, left out, and he would not join them now. The ignominy of being forgotten—how could he face it? He felt his heart go heavy and ache inside him unbearably. He lay down full length on the damp grass, crushing his face into it, no longer crying, silenced by a terrible sense of his insignificance.

I get the feeling that Ravi is experiencing a mixture of anger and depression. The anger I get from the fact that he refuses to join in the new game. He's doing what my own kids do when they don't get their own way. He's pouting, which I feel is a more angry than sad response. As for the depression, I get that impression from the fact that Desai writes that Ravi is not crying, yet his heart feels "heavy." Add that to the "ache inside" of him, and I get the impression that Ravi is angry and depressed over the fact that the kids still think of him as completely insignificant. He is completely crushed by the events, because he believed that by beating Raghu, he would be cheered as a conquering hero of sorts.

How does Anita Desai depict a child's development in "Games At Twilight"?

There are certain stages that we must all go through to become well-functioning adults who can live in our world and make a meaningful contribution to society. Unfortunately, often those stages involve a certain amount of pain and suffering as we have to learn some hard lessons about ourselves and our place in the world. This is the essence of this tremendous short story by Anita Desai, as we follow the protagonist, Ravi, going thorough one of these experiences. The lesson he learns is that he is not the centre of the universe and actually he is utterly insignificant in the face of the world and his friends. Note how excited Ravi is to find his hiding place and how he dreams of winning the game and the glory he will receive:

He hugged his knees together and smiled to himself almost shyly at the thought of so much victory, such laurels.

He imagines himself to be "a true winner, a breaker of records, a champion." However, ironically, although he is completely right and he does win the game, his daydreaming has allowed so much time to pass that the children have forgotten him completely and moved on to other diversions:

All this time no one had remembered Ravi. Having disappeared from the scene, he had disappeared from their minds. Clean.

Thus, as the children continue playing their funereal game at the end of the tale, Ravi feels he is unable to participate as he is overwhelmed by the "ignominy of being forgotten" and he is "silenced by a terrible sense of his insignificance." Thus Desai portrays this as a key stage in the development of all children, when we realise how truly insignificant we all are. However, with this humility, we are then able to mature and develop properly without thinking we are still the most important figure in the world. This is a painful but necessary stage for Ravi to pass through.

What is the theme of childhood in Anita Desai's "Games at Twilight"?

In "Games at Twilight" Anita Desai has the ability to portray childhood in all of its excitement and exhilaration, innocence, vulnerability, and even heartached.  The theme of childhood is one that encompasses all of those attributes, and is shown through the children themselves as they play a common and well-known game of hide 'n' go seek.  Childhood is exciting--you can sense the children's excitement as they are freed from the confines of the hot house and let out into the air to play.  Desai writes,

"they burst out like seeds from a crackling, overripe pod into the veranda, with such wild, maniacal yells,"

excited to be outside and free to play.  Excitement and exhilaration is also seen in Ravi as he finds an excellent spot to hide, and imagines his victory; he "shook, then shivered with delight, with self-congratulation" at his spot, and that the bully Raghu didn't find him.  Childhood is filled with innocence and vulnerability also; note the poor child that gets caught by Raghu, who ends up in tears as Raghu kicks him.  Note Ravi's happy innocent daydreaming in the garage as he awaits his triumph.  And then at the end, we see that vulnerability as his hopes are crushed, and Desai also brings in the theme of childhood heartbreak as Ravi learns a valuable grown-up lesson about his own significance:

"The ignominy of being forgotten—how could he face it? He felt his heart go heavy and ache inside him unbearably. He lay down full length on the damp grass, crushing his face into it, no longer crying, silenced by a terrible sense of his insignificance."

Childhood is filled with exhilarating moments of joy and glee, moments of vulnerability and innocence, and heartbreaking moments of difficult lessons learned, and Desai reflects all of these in her story "Games at Twilight."  I hope those thoughts helped; good luck!

How does Anita Desai vividly present the children in the opening of "Games At Twilight"?

The author effectively uses a number of various descriptors and figures of speech to indicate the children's emotions and actions and to graphically convey what they looked like. In effect, she appeals to the reader's senses and wishes us to indulge in these frantic and frenzied moments just before the children's release from the stuffy and stifling interior of the house into the exhilarating freedom outside.

In the second sentence, we learn that the children had been fed and groomed. They "had had their tea, they had been washed and had their hair brushed." The children were fed and clean, ready to face the challenges and excitement outside. They had been confined to the house the entire day since it had been too hot to play outside. They were impatient since the basics had been attended to. They were brimming with energy and ready to get dirty, as it were.

The author tells us that "the children strained to get out." The sentence conveys their impatience. They had been restricted for so long that they were, at that moment, striving hard to go outside, even to the point of exertion. The words "red" and "bloated" emphasize the effort the children put into their attempts to get out. They were like caged animals striving for freedom. 

Furthermore, the author expresses how stifling the atmosphere was inside by mentioning that the children found it hard to breathe. It "made them feel that their lungs were stuffed with cotton wool and their noses with dust." The only way it which they would feel comfortable would be if "they burst out into the light and see the sun and feel the air." The word "burst" suggests an explosive action. Once the children are let go, they will explode into the outside. If not, they will "choke."

The author makes it clear that the children do not even consider the mother's concern to safeguard them from the harsh sun. They just want to be out and beg her to let them go, making a promise that they will obviously be unlikely to keep, even though they counter the mother's unfinished phrase by stating that they will not leave the porch, as she evidently believes they will. 

Their pleading culminates in a what the writer describes as horrendous wailing. One can imagine the sound as being akin to the caterwauling of cats during the dead of night. Their terrible crying is what convinces the mother to let them out. Once the door is open, the children rush out "like seeds from a crackling, over-ripe pod into the veranda." The simile is quite apt and effectively describes their frenzied and uncontrolled rush to the outside. Once they are in the open, the children express their delight by screaming wildly and loudly, like a bunch of maniacs. They are ecstatic. 

The introductory paragraph evocatively conveys the exuberant nature of children. They possess a vitality that adults find difficult to understand. The introduction distinctly indicates how keen they are to be active and how much they despise being restricted. They wish to enjoy the freedom of the outside where they can truly indulge themselves. In addition, the introduction also establishes a contrast to the much more subdued situation conveyed later in the story, where the focus is more singular.