dnovraD: ??? Doom & Doom II, the DOS games, which predate controller rumble by literal years?
Presumably the version on Steam is using Steam Input or a source port which enables rumble.
They are not the DOS versions of the games. Doom + Doom II (alternatively known as Doom 1 + 2) is a 2024 compilation of the first two titles in the Doom series plus several mission expansions, including an all-new, 2-episode expansion exclusively for this release. Published by Bethesda Games, all of the Doom content has been ported to Nightdive Studio's KEX Engine for best performance, textures with special effects, and more complex map detailing, among some quality-of-life improvements. Released for Xbox Series X/S, Xbox One, PC, PS5, PS4, and Switch.
It has rumble on the Switch and the GOG version has it in the settings menu as seen in the screen capture.
I tried DS4Windows in multiple ways and it did not work. Someone tried telling me that the GOG version of DOOM + DOOM II doesn't support rumble which doesn't seem right since it’s in the options menu.