There is a very simple test to see if a game requires on-line access, and that is turn off your internet and see if it still works.

With NMS it will work, although you will miss out on a few features which have very little impact on the actual game (you can upload discoveries and get a few in game items for doing so) but the game will continue quite happily if you never once hit this function.

The statements made by GOG about this game are entirely true, and the OP might disagree with the wording but that is their problem not GOG's.

Simple test if you own the product, pretty hard if you do not, right?

Well it would be a problem for gog if they loose business because of it, also it is a problem for gog if someone wants a refund because of it, I do not find that statement entirely true on the basis of these contradicting statements.

GOG are very good with their refund window. If you buy a game which is marked as not requiring on-line access and later find that it does require it. I would fully expect they would refund you with very little fuss.

NMS does NOT require on-line access and it is perfectly possible for someone to download the game on-line and then never use the on-line services. You miss out on some minor functionality that adds a little extra to the game (but it is basically the equivalent of sharing photos taken in game to Facebook etc). Something that would not be missed if you could not do it.

You might not think that the statements are not entirely true on this basis but that is entirely on you. If someone claims a refund on the basis that it requires on-line access to access entirely optional on-line content they are really reaching for any reason to claim a refund.

But that's almost exactly what they have on the game page. It's right at the bottom of the System Requirements list and reads:

Please note: The GOG Galaxy Client is required to access online features for No Man's Sky

Yes, and are these lines not contradicting each other, where they say at the top, "no online connection needed" and then somewhere hidden at the bottom "online connection needed".

That is my issue with this whole thing.

OK, of course they are not contradictory...;) The SP game is DRM free no Internet access required. But you cannot play the MP game without going online...! Hello, knock-knock, anyone home?....;)

As I have mentioned before, MP does not mean you need an online connection, online MP does though, saying you do not need an online connection and then saying you do need it, is contradictory in my opinion.

Yes, that's true, and btw. for this special game I don't use GOG Galaxy and can still enjoy the online features, but of course I need to be online for that, no problem for me, but apparently a problem for OP who doesn't tell us the whole story about his problem, else this topic would have been solved for him after the 3rd response already.

@OP,
NMS is released as a single player game in the first place, although having online features. Please OP read the game features at HG homepage here, it will explicitly list what you can do offline and online:

https://www.nomanssky.com/release-log/