How do you picture a typical 3d shooter in 2d?
Well take "Space Gun" [my alltime fav!] arcade game for example: it LOOKS bit like 3D but it isn't. It has parallax walls and (quite badly) animated sprites to create a sense of 3D enviroment and movement, but it was 2D. And the only thing you (the player) could do was to kill the aliens and get more ammo. Co-op version with two realistic guns was a blast - literally! We had that (full arcade cabinet modified so that it was free to play) in our office for a while, too bad it's gone now.
http://www.klov.com/game_detail.php?game_id=9659