Because everything else in this game is so slick, it took me a while to realise why it all looked so funky...
Turns out, the game may cleverly default to 1080p, but at 4:3 aspect ratio, making everything stretched out, warped and otherwise unpleasant to look at. You definitely need to add a few basic video options to the menu. Install-and-go is all well and good, but not quite like this.
I just ran Doom2.wad so I could get to the video settings to fix it, then resumed the game as normal.
Edit: 'vid_aspect 1' in the console works too