Is It Possible to Beat Doom Without Firing a Single Shot? (2018) [video] (youtube.com)

TL;DR: Yes, dodge enemies and use shortcuts. Some levels require the use of glitches to make other monsters kill the final boss.

I love his comment "These can get you stuck for days". I wonder how long he had to play.

It's also possible to beat Doom2 without firing a shot, although you must go tool-assisted to exploit the random number generator to beat level 30. It takes nine minutes of setup to spawn all the Arch-Viles. https://www.youtube.com/watch?v=OpmPLrpGSos

B-b-but shooting is fun!

Reminds me of "pacifist" conduct in Nethack.