There's a very good book by Iain Banks called "The Player Of Games". About an earth games expert who takes on an alien at his own chess type game.
In one of the Asimov books,I can't remember which, he gives the actual moves of a game. A Ruy Lopez I think.
I know of the chess game in '2001: A Space Odyssey' but does any one know of other games in SF and perhaps has a 'kind of' internet with people playing games with other people in other countries? Would love to know... thank you gang.