I just followed the instructions on Mac Source Ports. I have Windows systems so is easier for me. Original Doom 3 bought directly from Apple back in the day. Doom 3 I did solely in macOS via an older Mac (32 bit OS) as Apple kindly depreciated the game

(not Apple's fault more the laziness of the publisher to update to 64 bit). Very easy as just copy the
base folder.
The BFG version was bought on GOG. I pulled the data files (
base folder again) from the Windows install and copied to macOS, hope helps

Both
RBDoom-3-BFG &
dhewm3 run really well on Apple Silicon under macOS 12 Monterey.
Think there's a note to create the data folder first then move to Library/Application Support as some have had issue. I didn't and was able to create data folders for both games directly in the Library.
If you get stuck PM me, I'll happily help...
Q-6