What is a suitable literary theory that can be used to analyse "Games at Twilight"?
I think using any theory based on psychology would be a good response to this question. There are of course many other possible theories that you could use to analyse this tremendous story, but, from my reading of it, its central message concerns the epiphany of a young boy who discovers a sense of his own meaninglessness and as a result grows up.
Let us remember what happens to Ravi. Hiding himself away in an excellent hiding place, he imagines the glory he will receive when he wins the game. However, when he rushes out, notice how the children and the setting are described:
Out on the lawn, the children stopped chanting. They all turned to stare at him in amazement. Their faces were pale and triangular in teh dusk. The trees and bushes around them stood inky and sepulchral, spilling long shadows across them.
To Ravi, the children appear "dead," just as he has been forgotten by them. In addition, note that the children are now playing a funeral game and singing a song that is about nature's indifference to human death:
The grass is green,
The rose is red;
When I am dead, dead, dead, dead...
All of this serves to highlight the epiphany of the final paragraph when Ravi is forced to confront the message of this incident:
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.
Ironically, although he rejects playing the funeral game, he does experience a kind of death: the death of his innocence and his hopes. Therefore, using a theory that focuses on the psychological development of Ravi would be important and productive in analysing this excellent story.