DOOM 2 has already been modified to suit every other franchise in the last decade, it only makes sense that the versatile shooter would get the battle royale treatment.
DooM Royale with Cheese does precisely what it says on the box. It's a multiplayer-focused fork of Doom that adds the nuts and bolts of a battle royale game: a shrinking map, hunting around for guns and picking your battles carefully.
DooM Royale runs off Zandronum 3.0, a multiplayer port of DOOM/DOOM 2 that supports up to 64 players. It's not the same as a 100 players in PUBG or Fortnite, but then, neither of those games have quite the same charm as oldschool DOOM.
For more info, and to grab the mod, head to DooM Royale's ModDB listing. You'll need a copy of the original doom2.wad file, either from Steam/GOG or the original floppy discs/CD.