comparison doesn’t really make sense - Poom runs on top of Lua, a very high level language, that would crawl on a 286 (if working at all).
see Doom machine specs to find the lowest cpu it ran on.
I think you're misunderstanding fredz72, so I'll try to clear things up.
POOM is a game for the PICO-8, which is a fantasy console (really a virtual machine and game engine) with certain restrictions in place so as to present itself as a classic 8-bit console like the NES. Those restrictions are arbitrary but hard-coded into the PICO-8 framework and unavoidable for any PICO-8 games as a result.
Ironically, the stated minimum requirement for running PICO-8 (and therefore POOM, albeit POOM is likely more demanding than most PICO-8 games) is a 700MHz processor.