Off the bat I was getting the old school FPS vibes, like doom and quake. The audio for the shotgun sounded great but it felt strange with no other audio in the game. Some ambient sound would go a long way, especially to create an adrenaline filled atmosphere as you're trying to escape a horde of zombies.
Lighting could have been more dim to reflect the environment of a ship, if you had blocked off the top of the level and baked the lighting it would have given you more opportunities to work in some point lights or spotlights to create that ominous feeling for the player.
When I fell into the pit of the green slime at the beginning I was just stuck down there until my health finally ran out, could maybe have the player respawn back at the top with a portion of health lost to indicate some damage taken but that you haven't failed completely.
Another indicator of health being lost could be a red flash around the edge of the screen like in doom as an example with perhaps a grunt audio just so the player knows that damage has been taken.
I feel that this has a great foundation to be taken forward though, it just needs a few tweaks to really take it up a notch.