Man, this is so much fun!
Reminds me a bit of the best parts of Chip's Challenge or Sokoban.
Simple yet addictive. Took me a while to properly understand how to play, but when I did, you totally understood what you meant in the game page. I suppose more people will go thru this "weirdness" phase, but I hope they all come thru and get to enjoy it!
Allow to add one minor nitpick: the pixel scales for the graphics don't match - so you end up with things that are super chunky and things that are very finely pixelated. Most people don't care, but when you match everything, it does look better.
Other than that, congrats - really nicely done.