The implementation of basic chess is pretty well done. Although I was able to trounce the "easy" AI and the game didn't seem to progress the difficulty at all (the only options after I won were to return to the Main Menu or restart the game.
The battle royal mode is a neat idea but I could never get a game to progress all the way through. Queens would often spawn in on the same square as rocks, rendering them invincible.
I'd always recommend adding some kind of AI to games like this, as it's hard to test out local PvP modes in a jam. Even some kind of system whereby P2/P3/P4 make a random move once per pre-determined "tick" would be nice.