mrkgnao: I plan to list here games that (at least for some people) clearly do not work without galaxy but do work with galaxy.
Ancient-Red-Dragon: How are we defining "work" here?
I think a game that includes a major bug in the latest versions that makes it practically unplayable, even if it is technically sort-of playable, is neither working nor running properly, and therefore could be said not to be working.
One game like that on GOG is Divinity: Original Sin. All the latest versions for the past two years include a game-ruining bug in it, which makes the tooltips for your skills not display properly as they were designed to do.
Due to this bug, you cannot see the level of the skill you are looking at, even though this is vital information that is 100% necessary to play & enjoy the game in a reasonable way, and it is information that you are supposed to be able to see, and that indeed you
can see
if you are using the earlier versions before this game-wrecking bug was patched into the game (yet apparently it will
never be patched back out of the game, as it already hasn't been for the past 2+ years).
Since GOG doesn't make the earlier & non-bugged versions available for download, then the only possible way to play a non-bugged version on GOG is by using Galaxy to rollback the game to an earlier version, before the bug was introduced. And even after doing that, there is still no way that GOG offers to
download a non-bugged version of the game in order to create a backup copy of the non-bugged version.
So for those reasons which I've just described, I think Divinity: Original Sin qualifies for the list in the OP.
Out of curiosity I just downloaded the most recent offline installer, removed Galaxy from my system and did a fresh install with the offline installer. everything ran fine, all the tooltips and UI ran properly with no issues.