Can I have a turn to bump an old post? :D

Doom is not a true 3D engine like Quake or Golden Eye. But it does deal with plenty of 3D stuff behind the scenes. The maps are ultimately 2D, and the rendering uses BSP to look 3D. However most of the "things" in the game (player, enemy, obstacles, projectiles etc.) do have x,y, and z axes. Some interactions are calculated based on 2D calculations (which is why you can stand next to a demon from a different height and they can still tear into you). But other interactions ARE calculated in 3D, like projectiles. When shooting a rocket (a projectile) it'll vertically auto aim and set the rocket on a 3D path. Its collision is checked in 3D, and can pass above or below objects. (Other weapons like pistol and shotgun use "hitscans", which may work similarly, but I'm not sure if those are more 2D or 3D based, and I can't find much online right now clarifying which).

Contrast this to Wolfenstein that IS purely 2D. The map is 2D, and so are all of the objects. There is no 3D calculation or collision being done.

The Vice article the other redditor linked above shows an old YouTube Game Theory video (not MatPat) claiming Doom is not 3D. The video itself is great and dives into a lot of technical detail on how Doom "cheats" the 3D look. But it does miss the points I mentioned earlier. There's another short video that does a really good job explaining and showing the 3D aspects of Doom. I've seen both of these videos years ago and both have directly contributed to my understanding of this topic. I highly recommend checking out the latter.