Simple, classic platformer gameplay. It controls well, however I'd suggest adding the option to control movement with WASD in addition to the arrow keys.
Also, a cooldown timer after taking damage from an enemy would make the game feel more fair by giving the player a chance to get to safety, instead of rapidly taking hits and getting a game over.
The dialogue adds some character to the game, maybe disabling any dialogue which has already played would make retries after a gameover feel less repetitive.