At least on the web build: When you die, go back to the main menu and then play again your score may say 0, but the next time you kill an enemy the score jumps to your previous + 1 (or maybe highscore + 1, hard to say as they will always be equal...) This obviously made the game less enjoyable than it would've been as you can't really fail to improve your score.
Now, on to the actual feedback: First off, I like how it looks and controls, though I do wish that I could just hold space rather than having to spam it. I also have a (weird) setup where I remapped some keys to my arrow keys because my laptop has those half up/down button keyboard designs. My browser reacts properly to it but your game does not for some reason. I'm guessing it is a unity bug?
The sound is pretty great, too bad there isn't music on the main menu. Would've loved to hear something of similar quality there :)