This is a really cool take on box pushing puzzles, I've never seen one where there's such a variety in how you can push them!
I do feel like it's far too difficult to read a puzzle at a glance. I don't know how much more of the game there is, but I think I've gotten pretty far. I've gotten stuck on one that has a few boxes set up in a chain reaction around the start. I feel like I'm thinking less about how to solve the puzzle as I am just trying to read it. It's hard to tell which box went where since they slide too fast, and you can't watch them all at once, so I can't tell which box did what.
Maybe I'm just dumb, but the way the arrows change on push was more confusing than helpful. It might be a hard to cram onto each box, but I think it may be more intuitive to give each box 4 arrows, one on each side, like this:
When you push from the left, the box will move in the direction based on the arrow on its left, and so on.