Interesting idea! I'm a chess nerd so idk if it will interest most people, but I did enjoy the aspect where you try to move your king/push pieces to protect you etc... (and obviously finding the mate). Some puzzles were very challenging, some others were weirdly easy/not elegant? Second level was hard, puzzle 3 was surprisingly easy (maybe it's just to teach player to put pieces to block enemies? I was already trying that in puzzle 2 lol). Puzzle 4 was devious. Puzzle 5 is really dumb (im having the intuition you dont really play chess lol). All in all pretty fun.
I think if you want to improve it it would be making the game/ui more accessible/adding some juice. Such as allowing arrow keys for moving, having some visual cues, like indicate visually that a solution has been found (and you need to press SPACE), when the solution fails have the black king show why it doesnt work etc (i dont think the pieces are very readable but heh), highlights the attacking piece if you try to move into check (or just show the squares you cant move to).
It's nice you did a single undo, but you can def implement infinite undos lol.
This sound for the king moving is just waay too loud.

