I have never installed GOG Galaxy on my computer before and I just did a scan after I installed Doom 3 "Classic Installer" version (setup_doom_3_bfg_1.14_(13452).exe), and found out that the "classic" installer put Galaxy folders on my computer located at:
...AppData\Local\GOG.com\Galaxy\Applications\50266185748810178\Shared\Files

Why is the "classic installer" putting Galaxy anything on my computer? No other classic installer has done this before, and I've never installed GOG Galaxy on this computer. If I delete all of those folders and run Doom 3 again, it automatically re-creates all of the Galaxy folders again. Has anyone else noticed this problem? I've attached some screenshots.

Strangely I did not have this issue when I used the "Classic" installer I downloaded off an Internet browser from my account. To test this, I made sure GOG Galaxy was completely removed from my computer by using Geek Uninstaller to remove all traces of GOG Galaxy from my PC, then re-installed Doom 3 BFG using the "Classic" installer, and GOG Galaxy didn't install itself onto my system after installing the game. Although I did see some *dll files relating to GOG Galaxy, the game was able to launch fine without forcing me to use GOG Galaxy from the game's executable or Start Menu shortcuts.

Furthermore, I think I may have found the culprit behind the game crashing on me when playing the GOG release of Doom 3: BFG Edition in that it may have been GOG Galaxy since the game didn't crash on me when attempting to play Doom 1 or 2 within Doom 3 BFG. I don't know if this is a sign that the GOG Achievements are broken or GOG Galaxy's installer broke something within the game and it's being delusional on what's broken or not when re-validating the game's files through GOG Galaxy. The GOG staff really need to look into this problem if people came here to get some GOG Achievements out of the game and their GOG Galaxy installer for the game are causing people like issues with playing the game when their non-Galaxy installer doesn't have these issues.

-EDIT-
Follow up on my issues with Doom 3 BFG on GOG, it seems that installing GOG Galaxy breaks the game because after re-installing the client I began having the same issues again. Getting rid of GOG Galaxy fixes my issues. Looks like I'm going to report this to the GOG stuff to fix their broken client breaking games they sell.

It looks like the devs forget to completely take out Galaxy from the game files of the Classic Installer. When I delete the GOG Galaxy folders, launching Doom 3 will automatically recreate the whole folder structure again. I wonder if there are Galaxy remnants elsewhere on the computer.

Are you deleting the Galaxy folder or uninstalling it? I completely uninstalled the client by using Geek Uninstaller to remove all traces of it and then used the "classic" installer to have it install under "C:\GOG Games\" instead.

That's the issue: Galaxy folders are showing up when I have never installed GOG Galaxy at all on this computer. But after I installed GOG's "classic installer" version of Doom 3, all of a sudden I'm seeing these Galaxy-only folders under AppData. That's why I was concerned that the game put Galaxy on my computer. If I delete all of the Galaxy-related folders and then run Doom 3 again, the Galaxy folders will return. It looks like a bug that needs to be fixed.

Okay now I'm seeing Galaxy-related show up in my local AppData folder, but strangely it's not causing the game to install Galaxy again on my computer. I deleted them earlier, ran the game, and those folders returned again in the same place.

Yeah GOG's version of Doom 3 is created these Galaxy folders even though the game was installed with a "classic installer." They really need to fix this bug.

Furthermore, I ran into this by trying by deleting/moving the Galaxy-related *dll files out of the game and this happens (see attachment). Not so "Galaxy-free" they say...

I reported these issues to GOG's support team, I hoping they'll actually listen.

Sorry for the double post, but there's another problem relating to achievements and GOG Galaxy as I installed the BFG Edition using the Galaxy installer on a different PC and this time the game doesn't crash but I get the "achievements are disabled due to developer console being open" except that I have the console completely disbaled in my config files, and I made sure to have the command parameter "com_allowConsole" set to 0 when I launched the game. So I'm starting to suspect that the GOG Achievements with this game are straight up broken unless someone else were able to get the achievements without their game crashing.

Maybe there's something internal it's required for? I mean think about it, Bethesda had their games with stuff like Steam rooted pretty deep in there for quite a long time.

It seems GOG doesn't get games without Steamworks to distribute either. Take a look at the terrible work they did to Worms Armageddon in removing steamworks functions that had modders pulling their hair out for a bit.

I also go this message, I think it was semi early into the game when I picked up a PDA?

Yes. Probably something to do with the way they prepared their software for Galaxy.

I actually got that message using a save from my game much further into the game when attempting to the game on my older brother's PC which showed that message despite that the console was completely disabled.