At one point in time let alone the Neo Geo, you couldn't even get it to run on the Amiga..
"The Amiga" is such a vague word. Which Amiga? There are dozens of different models with a massive range of capabilities or lack of. Not counting the hardware expansions and mods. The name is basically a platform, not a system.
I have been in many topics about the "Amiga" and how it compares to other systems or consoles and in almost all cases the posters can never stick to a specific system.
So no, DOOM can't run on the stock Amiga 500, which i assume is the machine most people are familiar with.
It also can't run properly on a stock Amiga 1200 either. Maybe a very low res version that looks and runs worse than the FX-Chip SNES one if you squeeze it hard enough.
If i ever see a DOOM port on the Amiga platform running and looking decently enough to worth the effort, i will automatically assume there is at least a 68030 CPU in there somewhere.
Yeah... using a device solely as an output device doesn't count as "running on it".
Not only that. Many "ports" aren't even close to being DOOM.
Like this for instance:
Or this:
These are obviously not DOOM. They don't run the DOOM maps, they don't run any engine that's remotely close to what DOOM does. They are so basic, even simple ray casters like Wolfenstein 3D look way more advanced.
But it's an "FPS", has the DOOM name and some assets that are based on it so it must be DOOM, am i right?
This is why the "DOOM runs on everything" meme makes me cringe. If it doesn't run the actual DOOM engine/code or at least a custom engine that does a similar enough job that allows it to run the original maps in a decent enough state that isn't as downgraded as to not resemble the originals, then it's not DOOM.