As a chess player i didn't have much expectations for a jam chess game, but it is fun. Fast chess is actually very popular on the internet, with blitz, and bullet time controls, and there even are competitions with ridicoulus time on the move.
I would love to play more polished game, with castling, en passant, and maybe a little limit on how fast the player can move, maybe " if you move, you have half a second of cooldown". (it may turn chess into some Crypt of the necrodancer spinoff as i think of it now)
Making a new chess variation is difficult and requires thinking outside of the box, and chess as a Real Time Strategy, instead of Turn Based Strategy is certainly thought of before, but don't give up, perhaps you will figure something new out.