TerriblePurpose: All I know is HG said they'd have multiplayer for the GOG version by the end of the year, implying that Galaxy can support it.
No, they said that they expect to have mp for gog by the end of the year. Not the same thing.
https://www.gog.com/news/no_mans_sky_next_update_now_live And the sentence about "joining forces" with gog to introduce mp suggests that while it's theoretically possible that galaxy could support mp, that might require changes, i.e. it can't support it presently.
TerriblePurpose: Also implying it's not actually GOG's fault. I don't know, but I think it's likely a little of both: HG probably concentrating on other things and making GOG multiplayer a low priority, and Galaxy maybe being a little more difficult to work with than HG was expecting.
Difficult to say whose fault this is.
NMS seems to be taking advantage of existing multiplayer capabilities on the other platforms it's been released through. That is fine and sensible. Especially with such a small development team and for a game which doesn't charge a subscription and hasn't charged for any of the major updates.
HG did flag their intention to introduce exactly this style of multiplayer long before launch. Presumably gog would have been aware of this and wouldn't have agreed to sell NMS if they weren't willing to support it. But we don't know that for sure.
We also don't know what kind of costs would be involved. Xbox and PS4 charge a monthly subscription for hosting multiplayer. Not only because they can but because there are genuine costs associated with that. Gog might understandably not be keen about shouldering those costs for NMS.