You are missing the point. It doesn't matter if Galaxy exists or not. And even less so on Linux. You are talking about a fraction of a fraction of a fraction of the PC gaming user base. The devs that would only offer 3rd party servers will do so either way. The only difference is that GOG won't be able to offer those games.

Realistically GOG is an afterthought. No dev is making decisions around GOG and even less so about Linux GOG users. If they can sell on GOG too, great. But no one is going to bend over backwards & change their multiplayer to do so.

Um how would that even work? How do you give someone servers or any guarantees about something you don't own & control? And there's no such thing as convenient multiplayer. It's hard no matter what.

I think you are making a faulty assumption that devs that only support 3rd party servers make a conscious choice to do so.

My argument is that in many (perhaps most) cases, the choice is made for them by the pre-existing bindings that stores like GOG or Steam provide.

You're not going far enough. I'd argue that in a lot of cases, multiplayer is an afterthought. It's not the main attraction, so devs are not going to bend over backwards to craft the idealised multiplayer experience.

They will use whatever existing tooling enables and existing tooling enables only integration with third-party centralised servers.

You publish a self-hosted implementation of the server-side (with modern programming languages, you can make it very easy for end-users to setup, often, it is just a single binary) that uses the same protocol as the centralised servers and you tweak the library bindings you provide for the url of the server that will be used to be a configurable parameter.

From there, the only adjustment the devs need to make is to provide users with a menu to either use the platform's centralised servers or enter the url for one that they are hosted themselves.

The end-user could run such a server across the internet or on their local LAN, thus supporting LAN multiplayer out of the box.

I swear to you, one day when I have more time...

I can tell you don't actually understand this stuff. So I'll stop here.

I'm not in the gaming industry, but I know a thing or two about networked software so try again.