That was awesome! I really enjoyed this and I'd love to see more of it, but I think a difficulty option would be pretty important so people who don't know chess could have fun with this too. (or maybe more of an open world type of thing where you can select which levels you wanna play (and at that point a level editor))
The description for the pegasus was missing the part where it can move 4 squares but I think that was the only issue I noticed, also maybe that one of the selectable upgrades was the one I already had.
I dunno if you need some ideas but I'll give some anyways, a powerup that would show the top engine moves once per game could be pretty interesting, also levels where the board isn't an 8x8 but something else, and maybe not even a square.
Maybe a piece that could revive a fallen piece on death, or maybe just a pawn. (Now that I think about it there were no pawns in the game)
Also, this might be hard to implement but maybe multiple opponents at the time and they'd fight against you and the other opponents, and then you could have a level where you're in the middle of a board and have to survive until the opponents battle it out.
And I think it would be pretty hard to balance some levels as the game continues so maybe levels where you have predeterminate pieces and you can only add a few to it from your army. (and at that point you might as well be able to add some to your opponent to counterbalance the fact that people will just upgrade all of their pieces)
Also, you could have squares that break if you stand on them for too long, and a river that pushes the pieces in them one square each move.
But yeah, very neat game, had a blast with it and I'm very glad I learned how to do a knight and bishop mate because I needed it here, although I just realized that stalemates are probably not a thing but I guess it's too late now, but yeah, thanks for the game!