That's curious to me. Doom is specifically not 3D. Was it a publishing issue (that Doom and co weren't produced for the Amiga), or a power issue, or something else?
The Amiga had planer graphics modes, while the PC/VGA cards had chunky mode (in 320x200x256 color mode).
It means that, to set the color of a single pixel on the Amiga, you had to manipulate bits at multiple locations in memory (5 in 32 colours), while for the PC each pixel was just one memory location; In chunky mode you could just do something like: videomem[320*y+x]=158 to set the pixel at (x,y) to color 158, where videomem would point directly to the graphics memory (at address 0xa0000) -- It really was the simplest graphics mode to work with!
If you just copied 2D graphics (without scaling/rotating) the Amiga could do it quite will using the blitter/processor, but 3D texture mapping was more challenging because you constantly read and write to individual pixels (each pixel potentially requiring 5 memreads/writes on the Amiga vs. 1 on the PC).
Doom's wall texture mapping was affine, which basically means scaling+rotation operations were involved. The sprites were also scaled. Both operations a problem to the Amiga.
As software based 3D texture mapping games became the new hot thing in 1993-1997, the Amiga was left behind. Probably wouldn't have been a problem if the Amiga has survived until the 3D accelerators in the late 90s.
This is quite well described elsewhere. Google is your friend if you want to know more! :-)
Also Amiga didn’t have hardware floating point whereas DX series of PCs in the 90s did. Essential for all those tricky 3D calculations and texture maps.
Quake has software full 3D which runs appallingly if you can't do fast FP, it's targeting the new Pentium CPUs which all have fast FPUs onboard, it runs OK on a fast 486DX but it flies on a cheap Pentium.
Doom is just integer calculations, it's fixed point math.
I didnt know Doom was all integer ... quite a feat.
In the general sense though the lack of floating point, as well as flat video addressing seriously hampered Amiga in the 3D ahem space.
EDIT I just remebered there is definitely at least one routine I know of that performs calculations based on IEEE 754 - “fast inverse square” or something. That could be at the root [badum] of my confusion vis-a-vis Doom ...
You are still getting confused by polygons. It was a 3D space that you could move around in. The matter of how it was rendered is an implementation detail.
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.
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.