Probably not quite enough raw MIPS in 1987, but people have since ported it: http://gerph.org/riscos/ramble/doomplus.html

Maybe it was more a lack of the DOOM source code or know-how?

According to https://en.wikipedia.org/wiki/Instructions_per_second#Millio... the ARM2 at 8MHz was 4MIPS. The 386DX at 33MHz was 4.3MIPS. The 8MHz 68000 was 1.4MIPS.

Of course there could be other things that made it hard, such as too few bus cycles when running the 8-bit chunky graphics mode? Or that sound did not use DMA(I don't know if the Archimedes had sound DMA) or that the CPU had to mix samples instead of the sound hardware doing it?

That was Zarch : https://www.youtube.com/watch?v=MNXypBxNGMo

This was the gold standard at the time.

Very much like the Zeewolf https://youtu.be/tVwScInZfP8?t=159

I wonder what the connection is.

Zarch : https://en.wikipedia.org/wiki/Zarch, 1987 Zeewolf : https://en.wikipedia.org/wiki/Zeewolf, 1994

The visuals look very similar, but I can't see any continuity in the wikipeadia article.

OTOH, the sqare grid terrain can be traced to at least https://en.wikipedia.org/wiki/Return_Fire although that was a sequel to a completely different game

Zarch was out out 1988, the port of Zarch, Virus, came out on Atari/Amiga a bit later, this came out 1995...

Chunky pixels? =) [1]

[1] https://www.youtube.com/watch?v=ACb0h7mmcQ8

Chuncky pixels refers to the "1 byte = 1 pixel" in this case, both the Atari and the Amiga had bitplanes, where the separate planes where interleaved into the bytes, this was a product of hardware limitations at times, for example using bitplanes you could do foreground graphics without the need to redraw the background graphics when the foreground moved, something that was valuable since the slow hardware (CPU and memory) could hardly keep up with the racing raster beam otherwise.