Not Doom, but a ZMachine interpreter might run with:

- Zork I-III

- Calypso

- Tristam Island

- All the Z3 machine games at IF archive

- The rest of Infocom propietary games

https://www.ifwiki.org/List_of_Z-machine_interpreters

Also: https://ifdb.org/viewgame?id=lkr2jf03np19ieix

Now, if the game was libre software it could be improved and ported to Puny Inform (a 'lite' version of Inform6 tuned for smaller machines) creating a really small Z3 file being able to play it from the PDP10 and 8 bit microcomputers to anything from today. From smartphones to PDA's to GNU/Linux with Frotz to Winfrotz and Lectrote and Fabularium for Android/Mac and iOS.

So, 'does it run Doom'? Man, you can play Zork in a pen with writting detection. How cool is that?