> gameplay-wise 3D is an illusion (no jumping, climbing or flying)

3D is an illusion in this sense in every game, with the potential exception of space combat simulators. And they can only make it work by pretending inertia doesn't exist.

You can fly in World of Warcraft, but all of the content is on the ground, and the designers keep griping about how they don't want you to fly because it makes them feel bad when you skip their content.

You can jump in Quake. You can't jump in Doom. This makes no difference. Level layout is the same. Jumping gives you the ability to cross very small walls and/or gaps, which Doom handles by simply not placing things to jump over in its levels. Elevation is real in both games; you can always walk up a ramp. There are three dimensions whether you can jump or not.

Doom is actually a 2.5D game and it cannot have free look or rooms over rooms. Quake can have both, since it’s genuinely a 3D engine.