I prefer the original Quake to Doom as the best arcade style FPS. Doom is too limiting to me in it's movement and level design. Quake still has the abstract level design and that makes it the only 3d FPS that I've ever played to make true use of 3d space. It's almost like parkour as you're flinging yourself from surface to surface, doing rocket jumps, all while spinning in the air and destroying hordes of creatures. It's Doom but more agile.
Rocket Arena! Yeah, Quake is insanely fast paced. I remember trying to explain this to friends playing FPS on consoles of the era (PS1 or PS2?) and just not being convincing. Even Halo felt glacially paced.
I've seen two mildly differing explanations for this particular version of rendering visuals being called 2.5D, one that it's 2.5D because the geometry looks 3D, but the actors are all sprites, the other is that the geometry looks 3D but it's actually a 2D floorplan with tricks to simulate different heights.
There's also at least one another unrelated "2.5D" use, when the world is 3D, but the player moves on a strictly 2D plane.
Also the fact that the player would just look straight forward the whole time, so when shooting at an enemy at a higher/lower elevation you just needed to overlap him on the X coordinate on screen.
Probably. To be clear, what's being stated here is that Doom, Wolfenstein, etc. don't actually render from 3D internal data structures like Quake and later first-person shooters did. The level layout is inherently 2D and some tricks are used to render the environment in a way which looks like a 3D perspective. But it is fundamentally a sort of flat-lander's pseudo-3D.
