Getting touched by an enemy and immediately sent to the main menu can get pretty frustrating since it makes it much harder to tell how I died and it makes me sit through the short cutscene with the chair each time as well.
Locking the cursor to the game window would be nice as well because my dual monitor set up leads to me clicking outside of it pretty often. The cursor being the same red as the walls doesn't help with that either.
The gun play itself could feel more satisfying if the player's bullets went faster, and whatever they collided with had effects going in the direction of the bullet (i.e. blood, debris, etc). The corpse is a good idea and you could go even further if you emulated what Hotline Miami did to juice up kills.