It does check if you have a license through GOG, but it only cares about that for the auto-update features of Galaxy. It still lets you play the game just fine.

Looks like the game is peer to peer, so LAN play is possible in theory.

It does not. It checks if your account own that game (then enables auto-updates and other account linked things) but if you install GOG game via installer it will be shown in galaxy and playable even if you do not have that game on galaxy logged in account.

Multiplayer playable right?

So they couldn't seem to THINK AHEAD and have GOG get programming the multiplayer part or setting it up before the 1.5 patch?? Really?

any mention of LAN support for this game?

My question to the dimwits in here whinging at the Galaxy requirement and insulting others is the following: How do you then prevent rampant piracy of the GOG version ? I mean you literally give a in to the multiplayer for anyone with a GOG copy (legally or illegally obtained) if there's not some form of gate in place. The honour system doesn't really work here as it would with SP only games.

You're right. So why are people so dead set expecting Hello Games to have everything ready day and date for the GOG version? Like mentioned in the Noclip documentary on GOG on YouTube, GOG in many cases has to convince developers to come to the platform. In a lot of cases, that means someone, be it GOG or the developer or both, doing extra work to make a GOG/DRM-free version. Could Hello Games have held off until multiplayer was ready for GOG? Yes, but every day that they wait leaves the game less and less relevant once the update launches.

Back in 2012, there was a debate on the Stardock forums for Sins of a Solar Empire when Rebellion was announced to be releasing as a Steam exclusive. It was a big concern for at least some people who only found out when their cards were charged for the pre-order and they were given an email receipt with a beta key for Rebellion on Steam. Among other things, it turned into a debate about Stardock's touted Gamers' Bill of Rights, the accusations about which drew particular ire from Stardock's CEO, Brad Wardell (Frogboy on the forums), who at one point chimed in to say, "I don't think the anti-Steam demographic is large enough to justify giving it special attention. In fact, I know it's not."

Fast forward a few years and Sins of a Solar Empire: Rebellion and a number of other Stardock games begin releasing on GOG. What changed? To use some of Frogboy's words, the anti-Steam/DRM-free demographic became large enough to justify giving special attention. Is there parity between the Steam versions and non-Steam versions? No, or at least not so in a number of cases. The only way that's going to change going forward is if we as consumers continue to give developers cause by being a large enough and engaged enough of an audience to justify putting more focus into.

So when features are missing compared to the Steam version why the game cost more here?

No Man's Sky refunds:

https://www.gog.com/forum/general/extended_refund_policy_for_no_mans_sky_f8934

DRM free multiplayer on GOG? not in galaxy's backyard.

What do you expect GOG to do? Hello Games is refusing all refunds, at least GOG appears to respects there customers unlike Hello Games who again chose to conceal important information pre release.

Go ask Hello Games for a Steam key?

This shows me that GOG seems to have absolutely no control over the companies that sell games on GOG. These companies like Hello Games can do (or sometimes not do) what they want without any implications. Deliver a half finished game or, as it seems in this case, tell GOG 4 hours after release that one major aspect of the current patch will be delivered some time later.
What to make of this is up to every single one of you. I made my descissions some time ago.