Doom was a 2D space that looked like a 3D space due to rendering tricks. You could never move along the Z-axis though because the engine doesn't represent, calculate, or store one. That's why you can't jump, and there are no overlapping areas of the maps.

Regardless of the “technicalities”. My point was that this, and other 3D games were something that Amiga could not do well - whether 3D, or “simulated 3D”.

It really wasn't. Doom's gameplay almost entirely took place in a 2D maze with one-way walls. It was rendered to look 3D, and as you said, that's an implementation detail.

You coudn't look up and down, neither you could do with DN3D.

I am not confused, the opposite. I grew up with that.

You can look up/down in Duke3D, its under home/end keys. It doesnt look pretty nor correct, but you can do it.

I grew up with it too ... I disagree with your categorical boundaries. The distinctions you draw are purely technical.

purely technical? You can't go above or below anything; no two objects can exist at the same X/Y; height doesn't exist in any true fashion (the attribute is used purely for rendering --- there is no axis!). How is the existence of the third axis in a supposedly 3D environment purely technical?

With only two axis, it is literally a 2D space, which gives some illusion of 3D as an implementation detail --- not the other way around.

It isn't "literally" a 2D space. It is "topologically" a 2D space in that you could represent it as a 2D space without loosing information. It doesn't provide 6 degrees of freedom but it is very much experienced as a 3D game environment.

EDIT also, using the term "literally" to talk about 3Dness when it is all rendered onto a 2D screen, is fairly precarious. No matter how many degrees of freedom, or how rendered, it will never be "literally" 3D, in the literal sense of the term.