First I was doubtful, whether this game was good... But, boy, was it good. The puzzles were great, you balanced the difficulty really well, and did the introduction to the game pretty well. But somehow I feel like this came from a board game designer, not a computer game designer.
I'll start by why I think this is the case. If you were a complete beginner at game design, I don't think you would have made a game this good... BUT! There are some pretty important things for computer games. Do not use unnecessary amount of buttons. All this Q and E hassle was a mess. You should get rid of either of those keys. Maybe even both. You could get rid of Q like this: You press E to see the laser, then you press E again to continue/restart based on whether the player have failed. And you should clearly indicate it on-screen, whether the player has or has not failed. But what I would actually favor over this would be adding the option (Maybe E) to make the laser. But when the player has run out of moves, you clearly indicate that, and by pressing a directional button (or E) it starts the laser. And with this, directional keys and space could also restart the level, since the have no other use case either way.
And with this I'll continue to feedback. If the player does something, if something happens, add feedback. When the player fails, there is pretty much no indication on what happened. The board just resets. One way to counter this is to make the move counter actually count down as the player is making moves. You could even add some additional effects to it when there is only one move left (but don't go overboard with it.)
This is why sounds are also so important. They are a simple yet effective way to give feedback. A satisfying sound when the player succeeds. A neutral sound when the player fails, like a simple whoosh sound. (I wouldn't recommend a negative sound in this kind of game, since it would make failing the puzzle feel worse.)
Once again, I just wanted to clarify, you made some amazing puzzles, which many people could learn from. I just wanted to give you some useful feedback, so that you can make your next game even better.