(It only seems to work in Firefox, though.)
Doom, rendered into a browser favicon. Also rendered in the document itself so you can usefully see it.
Had to be me. Someone else might have gotten it wrong. ~ Mordin Solus
JS-DOS renders to a canvas object, toDataURL converts canvas objects to a data URL, Favicons can be set to a dataURL. It's just chaining it all together.
Without the existence of Defender of the Favicon I probably wouldn't have realised this was possible. Also to this StackOverflow answer, which sent me down the rabbit hole. This gist from Mathias Bynens also made it all way easier. And of course this wouldn't be possible without JS-DOS.
Doom is owned by id Software; this repo contains the shareware version of Doom, compressed in .zip format. If you want to play the full version of Doom in your favicon, you can buy it from GOG here and then modify the .zip location referred to in the html file. Though that is probably not the best way to experience Doom.