i don't think you can move up and down in Doom, but no-one would seriosly say its not 3D.
3D is not about how you can move.
Its about whether depth is show on screen, and how this depth varies to mimic the real world as the viewing perspective changes. Look at a cube for example, as you move around or "above" it you see all of its sides,and the top and bottom and the view changes to match your viewing angle as it does in the real world. Limiting your view to only horizontal and vertical viewing positions doesn't stop it from being 3D.