Uninstall games and Galaxy.

Download GOG Galaxy installer start it as admin and install Galaxy to path C:\Games\GOG\Galaxy\.

Exit setup. Set Galaxy.exe runasadmmin in properties.
Reinstall game (reset default path in Galaxy settings) to exact path (C:?)X:\Games\Quake-4\.

If you plan to play game only from Galaxy - you almost ready to go (*). If you want start it also directly from exe\Windows Start Program - Programs - menu links - set quake4.exe adminrun.
Better do that for every games and their external settings tools. Editors or Dedicated Servers executable;s not needed that.

* Always do verification files for any downloads in Steam, Galaxy, Origin\etc, BitTorrent\etc and everywhere where it possible. For Steam better at least twice. Steam should tell you thta files are passed checking - no downloading. Galaxy previously work same, long ago. Now this function is broken - Galaxy not tell you result. And galaxy always redownload redists\dependencies recreate links and so galaxy even if report something - it be anyway reports of something downloaded. So always do at least twice check after installation, in case if first one is really do redownload-correct some files.

If you use antivirus - make sure it not affect Galaxy and games. Windows Defender with default setting allow Galaxy to do anything with games and anything for games if you start it from admin - that also affect Defender.

Any compatibility\affinity\etc set to exe (before or after launching for e.g. core affinity) also be set to any exe started from initial one. And Defender pass any exe if initially it be adminrun with UAC prompt asking you about permission (better keep it that way, do not turn it off).
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Or use GOG Galaxy to download offline build. Still - start adminrun installer and set quake4.exe adminrun - even for X:\Games\ folder.
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You dont needed any tweaks tools (downloadable). Just fix one(two?) string in CFG settings for normal graphics on modern GFX card (default set to low cause of incompatibility).
First properly set settings ingame. Make sure you set resolution that supported by display (eg 1600x1200 is way more than fullhd).
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UPD: Oh yeah. And make sure there is no other compatibility chekcboxes enabled. GOG previously put only admin run. Now they put fullscreen optimisation instead of admin run even if it not needed - it work very differ on differ OS\builds.
You should experiment with that only if you really have glitches with screen ingame.