That galaxy binary/shortcut only runs because the galaxy system service is running. If you uninstall galaxy-client entirely, you cannot run the executable for the game any more.
This is fact and the last time I tested it with was Elex, because of the same reason to get an update faster.
In case of Elex, there is another game executable that starts even without Galaxy, but I would not bet on it for every game.
I'm not sure how people get such a simple thing so confused, but OK, I just did two things...;) Sounds like you are getting the Galaxy-made game shortcut, which runs Galaxy first because Galaxy is in included in its pathing via the shortcut properties, mixed up with the direct exe shortcut, which you have to make yourself, as I previously mentioned in the last post. (The exe shortcut does not mention Galaxy anywhere in its path, which of course means that the exe shortcut never invokes the galaxy program. Obviously.)
(1) I ran D: OS2 from the exe shortcut, bypassing Galaxy completely (shortcuts made from the game exe do not reference Galaxy at all). Game ran fine, as usual. I alt-tabbed to Windows, I opened Taskmanager, saw that the Galaxy communications service was running, and I ended that service by closing the task, and alt-tabbed back into Divinity OS2, and continued to play with no Galaxy services running at all.
(2) Next, I opened Services under Windows and disabled both the Galaxy communications service and the Galaxy client service, and then *rebooted* the system--very important step when making registry changes. When it came back up I ran the game again from the exe shortcut Eocapp.exe. Game ran immediately without any problem whatsoever. Alt tabbed into Windows with the game running, checked Taskmanager again--no Galaxy services running at all. (Indeed, my stock Windows services config has both Galaxy services set to "manual" which means that they only time they run is when Galaxy itself is run.)
The problem people evidently have is they keep forgetting that GOG does not offer DRM to game devs *at all*--and there are no GOG games that use/force DRM. None. Steam offers game devs DRM if they want it--and often developers who sell on Steam choose not to use Steam's DRM--I have several AAA titles released in the last couple of years that can be run directly from their exes and Steam doesn't run at all when the games run (Witcher 3, Pillars of Eternity, and several more)--*unless* the customer wants it to run and he runs it.
Many other Steam games, however, enforce Steam's DRM, and cannot be run outside of Steamworks. Again, GOG and Steam are *not* equivalent on that point--GOG *never* allows developers to use DRM. Galaxy, is *not* DRM in the sense that Steamworks serves as DRM for the game publishers who wish it to. That is why several AAA titles don't come to GOG at all, or else years after they ship--the dev/publisher insists on DRM and only Steam offers DRM to developers and publishers. I have also noticed of late that developers who sell their games on both GOG and Steam (inXile, Larian, CDPR, etc.) mandate *no DRM* with their Steam titles, too--so as to be equal as to there being no DRM on either game version--Steam or GOG. That's only logical, of course.
So, anyway--I hope we can finally put this to bed...;) Galaxy is not DRM as Steamworks often serves as DRM. The two are not equivalent on DRM. Steam uses it; GOG does not.