Original DOOM and DOOM II game engines were 2.5 D.
You could not look up and down or jump.
That is not to say that there was no z-axis in the maps themselves, but the game engine handled it in a simplified, flattened way.

Its been a really, really long time since Quake z-axis code was backported to create zDOOM.
You are a great example of people not realizing this.