Some very minor criticisms:

1. I would love a reset level button instead of just a reset game button.  When I know I've messed up, it would be nice to not have to die on purpose and wait for the turn to resolve.
2. movement selection could use some tweaks:  Its a little weird that the rook always defaults to the square above it but the pawn defaults to the one below it.  It would probably also be better if the cursor snapped to the possible moves instead of giving you full free movement
3. Subjective:  It's a little weird to me that you are forced to move your pieces into threat, but the AI will skip its turn rather than do the same when at the start they will happily march off of a cliff.  The early levels trained me to think that I could rely on pawns always moving forward no matter what, so when I came up with a plan to trap a pawn and it didn't move, it felt a little unfair.   I'd probably rework the early levels to remove the bottomless pits, or maybe get rid of them altogether and introduce the rook earlier.  Personal preference, so disregard if that's part of your intended difficulty ramp.