The what? Can't blame you if the name "Vectrex" doesn't ring a bell. It was a gaming computer released in the early 1980s that featured vector graphics (lines and geometric shapes). It wasn't exactly the most colourful of systems — in fact, you had to use special overlays to get anything other than black and white — however, it was considered rather neat for its time.
Anyway, Doom. There's a video on a YouTube channel by the name "Sprite_tm" that shows a Vectrex playing "Voom", an extremely lean version of id's opus. If you've played Doom, you'll recognise the geometry of the first level, even if it's missing, well, everything else. There's also no collision — you'll notice the player clips through a wall early on in the demonstration.
It may lack imps and shotguns and be barely playable, but it's still a cool little project.