Nice little doomesk concept! I think you could improve on this in a few ways.
I would remove the ability to look up and down. Bind your movement to AWSD or arrow keys . this will make the game feel more natural. You don't need vertical movement in this style of game.
lastly i know its a joke, but i would actually place the gun in the center of the screen. I think it would work better as far as aiming goes while you play.
great job!