Ok well I wrote a nostr chess server and a command line client and I played a game of chess with myself (the library that manages the game state and legal moves and stuff was written about a month ago).

The nostr events I'm using (all ephemeral) are documented here:  https://github.com/nostr-protocol/nips/issues/1453

The server is running in case anyone else wants to write a client:
   pubkey of the chess server:  dbb45efeb8cc10e6f75fdff7e561e7db39cc7ba6592f4c22e26f3ee36b2e7bc2
   relay it is running on:  wss://chorus.mikedilger.com:444/

If it stops responding, get in touch with me and I'll restart it.  I'm just running it from a terminal and I may forget about it and reboot or something.

I'll bet some brilliant graphic designer out there could create a beautiful client where the pieces slide, there are noises, the square it came from remains highlighted, all that jazz.