Well it's difficult to classify now. The game play in doom is 2D, viewed in a limited 3D representation. The engine is designed to exploit the 'lines of equal z' optimization. As a result, It's one of the first games that i can think of that included perspective correct texture mapping. Which was considered not to be viable for real time use then, as to work out a perspective pixel your constantly dividing the UV cords by 1/Z (from memory) (you can reduce that to by only calculating perceptive points at predefined points along the strip then interpolate between, which is what Quake does) . Division was ultra expensive in then (386/486). So most texture mapped games used 'linear texture mapping'. Which gives a PlayStation 1 look to them. Since it doesn't has perspective or z buffer support.
The lines of equal z optimization gives the ability to calc perspective only along the wall/floor edges then linearly interpolate between the edge points. All the pixels in the strip can be interpolated, as the Z will be uniform (does not change). So It's very quick and looks convincing to the eye. The restriction is that the scene must not rotate around more than one axis at a time. Which would break the optimization. The Look up/down features in Doom is just a fudge.
Replicating Doom as it was done, would be a
real challenge. Even with hardware support for rendering there's still collision, visibility not to mention building the geometry.
Could be fun though.
