I've asked repeatedly in the release thread if anyone knows whether the daily challenge mode can be used without Galaxy installed (also wondering about co-op mode, though that's more out of idle curiosity than any likelihood that I'll be playing multiplayer); no one (including GOG staff) has given me an answer there yet, and while I did also create a thread about it in the dedicated forum, it could be months or years before anyone notices it (without help), and I'd rather have the answer while the discount -- and, ideally, the #SummerGaming sale -- is still on.

So, if anyone knows the answer, please reply in the topic I linked to above, so that I can mark it as "Solved" and you can get some sweet, sweet Meaningless Internet Points. :)

First, co-op is local only so it shouldn't matter if you use Galaxy.

As for the leaderboard and challenges, I'm not sure. It seems to pull info from Galaxy after it's installed and uses your username for the leaderboard. They seem to work fine without Galaxy running but I don't know if they will work without Galaxy installed at all.

I don't have a clean machine to test it on at the moment either. Uninstalling Galaxy isn't something I want to do just to test one game either - any game that uses Galaxy will probably break if it's suddenly missing.

Sorry I can't be more help.
Hopefully a blue can help you out.

Good to know. At least that's something. :) Someone told me something to that effect in the release thread. It makes me think that leaderboards (which I don't really care about) require Galaxy, which suggests that the daily challenge mode does, too. Still, I'd like confirmation one way or the other before I (potentially) pull the trigger on it.
Still, thanks for checking.
(I'm not holding my breath waiting for a reply from a Blue, considering I replied to both the GOG.com "Editor" account and JudasIscariot asking about this in the release thread, and have yet to get any response. :\ )

Never mind, I see they've silently added a small disclaimer to the game's store page at some point in the last couple days. Galaxy is, indeed, required for the Daily Challenge Runs. :(

I just fired up the game without GOG Galaxy and went in the daily challenge door and it seems to have worked fine.

Then you must have Galaxy installed. I don't (and never have), and the door's not even open for me.
Anyway, I already got the answer (and went ahead and bought the game anyway).
Still, thanks for trying. to help :)

It's installed, but it isn't running, unless GOG has some other processes that stays running in the background when their app is shut down. If that's the case then I'm uninstalling it right away.

I don't open GOG Galaxy unless I hear of an update, since they don't post patches anymore.