Wow, looks so minimal yet so amazing! I liked the design. I liked the choice you made about enemy colors. They are not glowing shiny targets to hit, you search through squares to find an enemy and shoot before it. Well thought!
I also liked character moves in arc path instead of line, I think that would kill the feel of this game. Because sometimes I try to slip through the boxes while shooting the enemies.
If you want a feedback, I would suggest you to add an indicator to where player is going. For the reason our character is a rectangle, moving can sometimes hard to predict. Here's what I mean:
You can add a line that shows where you are going, and when you get close to a wall, it may start to turn red. For extra mechanic you can make this line able to clean through what's on its road. Maybe this decision can break the game logic but hey, it's just an idea from random internet stranger after all.
Good luck on your project, this one is indeed a spectacular entry! Have a great day!