Really cool idea! Having a chess dungeon crawler is a neat idea that I don't think I've seen explored yet. It's smart because everyone knows chess so they don't need to learn how each piece moves.
Here are my issues with the game / areas of improvement:
1. With each player only moving one piece per turn, the gameplay feels a bit slow and formulaic, since there isn't much either player can do to strategize. It would be cool (although less chess-like) if each player could move 2 or maybe 3 pieces per turn, would allow a lot more strategy within the turn like "ok ill move my queen out then move my bishop over to heal it". This is partly involved with issue 2
2. I wish I could see the enemy's pattern of movement, because it is really hard to plan ahead when you don't know where / how far the enemies are going to move.
3. The tutorial is a lot to take in at the start, a whole lot of words on the screen at once. I think instead of having one huge text dump at the start it would be more useful to just have tooltips that show what the empowered moves do when you hover over it. And I don't think it's necessary to explain how each piece moves since most people know, and leads to some visual clutter.
Overall though very well done! I would definitely buy this type of game if it was fully developed into a product!