Please navigate to the game installation folder(default: C:\GOG Games\DOOM 3 BFG\). If you are using GOG Galaxy, please select the game, press MORE -> manage installation -> show folder. After that, please right-click on shortcut, select properties, add: +set r_fullscreen 3 so the entire line will look similar to this: "C:\GOG Games\DOOM 3 BFG\Doom3BFG.exe" +set r_fullscreen 3
If you are launching the game via GOG Galaxy, you can add command line arguments.
Please launch GOG Galaxy -> select the game -> press more -> settings -> select: 'Add command line arguments' -> add: +set r_fullscreen 3
Afterwards, apply changes and try to launch the game.