Didn't expect such a cool chess-based game! I'm also a big fan of your level and puzzle designs. The art style is cute, especially the animation of the chess pieces,well done! :)
Are you planning to add other chess pieces? For example, the queen, or even some pawns, and play with variable square moves? Since pawns' first move can be one or two squares (you could even play around with en passant if you plan to include enemy-based pieces), or maybe play around with dark and light squares by adding boosts in the form of multipliers, where a piece gets more stamina? :D
One last thing:
I found myself clicking the princess herself a lot instead of the blue play button. I feel like your game could use two play buttons simultaneously: one is the main blue button, and the other is the princess itself.
Great job, congrats! <3