Wow, this is a great use of dual purpose design when it comes to rules/systems tied to a mechanic. The only thing I would maybe change to reinforce dual purpose more is having one button like space bar be attack. So you either attack in the direction you're currently moving towards or in the last direction moved towards before stopping. Moving diagonally would prevent you from attacking in this case.
Otherwise, aesthetic(visual and music) feels very cool. Reminds me of Invader Zim. I like the attack sfx for the player too. Some different enemy types to change how you balance moving/ stopping and attacking and this would be even better!