How is the theme of loneliness, in your opinion, dealt with in "Games at Twilight" by Anita Desai?

That's a good question because that is not one of the typical themes that gets focused on in this story.  

I would say that the theme of loneliness is dealt with and best illustrated through the character of Ravi.  Desai includes subtle details in the story that highlight how and why Ravi exists on the outskirts of the group of other children.  We know early on that Ravi is not a physical powerhouse of a child, so he is not the group's popular "jock."  

. . . but he hadn’t much faith in his short legs when matched against Raghu’s long, hefty, hairy footballer legs.  

Actually, the very first detail that readers are given about Ravi portrays him as that "weird loner" kid.  

Ravi heard the whistling and picked his nose in a panic, trying to find comfort by burrowing the finger deep—deep into that soft tunnel. He felt himself too exposed, sitting on an upturned flowerpot behind the garage.

I'd like to point out that Ravi is sitting, alone, on a flowerpot behind the garage.  He is not where most of the other kids are.  Additionally, he is picking his nose, and trying to find comfort in that activity.  It's the equivalent of a small child sucking his/her thumb. That is not something that wins over large groups of friends.  

Another loneliness detail is the game that the kids are playing.  They are not playing a team sport in which every kid is part of a team that works toward a common goal.  Instead, they are playing hide-and-seek.  That is an inherently lonely game.  One person is "it," and everybody else is supposed to find their own hiding spot.  Nobody hides with a partner in that game.  It makes you easier to find.  

The best evidence for loneliness and Ravi's embodiment of that theme comes at the end of the story.  Ravi has been hiding, alone, in the shed for hours.  When he finally comes out to claim his victory, nobody believes him.  All of the other children have moved on to a different game.  Nobody knew that Ravi was still playing.  They completely forgot about him, and that shows Ravi how little attention the group gives him.  He has been left out yet again.  He feels completely alone and insignificant, and Ravi goes off alone to quietly sulk.  

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.