They work from the console prompt now for whatever reason.
Editing the config file or otherwise trying to enable the console that way won't work as the file will regenerate (And thus erase that line.) when you next exit the game but I got around that by using one of the existing config files in the game folder.
joy_360_0.cfg (I guess one could also simply write them into default.cfg directly.)
Added this to it.
//EDIT exec test.cfg (At the bottom on a separate line // is just so I know more clearly what I altered.)
Then I made a copy of that file and called it test.cfg and deleted everything in it and put in the commands I wanted.
set bind home toggle g_showhud set com_allowconsole 1 set com_skipintrovideos 1 set g_nightmare 1 set g_roenightmare 1 set g_lenightmare 1 set g_infiniteammo 1 set g_showplayershadow 0 set g_skill 2 set g_fov 90 set g_gunscale 0.5 set image_highqualitycompression 1 set pm_thirdperson 0 set pm_thirdpersondeath 0 set r_maxanisotropicfiltering 16 set r_customheight 1200 set r_customwidth 1920 set r_windowheight 1200 set r_windowwidth 1920 set r_overbright 1.0 set r_lightscale 1.0 set rs_enable 0 set win_allowalttab 1
You only really need this "set com_allowconsole 1" albeit this "set com_skipintrovideos 1" can be useful too. (Rest are just a bunch of smaller tweaks and changes for what little is actually possible to alter compared to the original IDTech4 version of Doom 3 but it's something at least.)
EDIT: Right you can just write id in the console prompt and press tab and it should display all of them, iddqd is misspelled as idqd just so you know, guess they missed that second d letter.
The game saves a config file here: C:\Users\Jonas\Saved Games\id Software\DOOM 3 BFG\base (User name will differ for you depending on what you named the account.)
It's called D3BFGConfig.cfg and it is rewritten each time you exit the game so any extra editing will be deleted and lost if attempted here which is thus why I opted to edit a existing config file (Which is never altered by the game.) to force a exec command of yet another file (Minimal editing on existing files, safer too.) and then get that file loaded into the game with the custom commands I wanted to use.
It's similar to user.cfg for Battlefield 3 / Frostbite 2 or system.cfg for Crysis / Cry-Engine. (Or even RageConfig.cfg for Id's RAGE / IDTech5 game which is why I tried it here as well since it's the same engine.)
I am however not very good at explaining stuff and it gets a bit technical as well so while I can understand it myself others might have difficulty following the instructions.