Doom was kinda 2.5d, not 3. They swapped out 2.5 d levels when you entered an area where you supposedly overlapped the map in the vertical axis. Other games that came out around the same time include worlfenstein 3d (also 2.5d, plain floor iirc), ultima underworld (not full screen) and system shock (full 3d, but always oriented to the user, with feet on the ground). Only descent went full 3d, but was disorienting to some users. Dooms tour de force was the optimization and the fps/ immersion it achieved, and we have carmack and his work on raycasting to thank for that, on (you stated) non accelerated hardware.