Competitive chess playing is very resource intensive: fastest multicore processors, gigabytes of hash tables for middle game, hundreds of megabytes for opening books, tens or hundreds of gigabytes for endgame tablebases (6- or 7-piece respectively).

You would have to come up with a different chess game scoring system that doesn't take account of time.

Also, chess has no hidden state, so what would be benefit of using the zero-knowlegde system in the game?