Also no mention on the store page that the co-op doesn't work without GOG's Galaxy DRM platform.
Now, that one is just a matter of requirements by now. You can thank Steam for that one. (But arguably it was inevitable, if it hadn't been them, it would've been invented / introduced any of the other platforms.)
To explain in an oversimplified manner... the game does not have it's own multiplayer code. The multiplyer code is only provided as a plugin, by <Steam / Origin / Epic / GoG>, which need a dedicated client with a friendlist for matchmaking to work, because that's how Steam did it, and what the games embraced as a standard. (Kind of like 3rd party controllers are all mimicking the Xbox controller protocol.)
The good side of it is, 1) this makes it easier for games to offer multiplayer, as the devs don't have to develop it, and 2) nor do they have to host the servers for it themselves, enabling even small devs to create multiplayer games. They just use <Platform>'s plugin that's provided to them, and don't have to deal with anything else. It's a puzzle piece that slots stright into the game. Multiplayer, done.
Now when a game gets released on a different platform, that puzzle piece obviously can't be taken with, and needs to be swapped out by the one of said platform for multiplayer to function. GoG didn't have one for the longest time, which is why games used to release on GoG without multiplayer support, at all. The puzzle piece simply didn't exist, and it left a hole.
This is the nature of outsourcing multiplayer infrastructure. It's cheaper and easier for the devs to do, but requires the player to be using a client as the game does not have accounts, friendlists, nor multiplayer code of it's own.
Steam invented it, it took off big time, and everyone else can't do anything about it but provide their own puzzle pieces to slot in, or alternatively, cut multiplayer alltogether. It's not been designed as a DRM measure, but as a service to game devs.
Some games do still have their own multiplayer code integrated to this day, like Factorio which will prompt you to create an account with the devs ingame, or Project Zomboid, which even provides a dedicated server for anyone to run. But they are rare, because it's more effort and costly to develop, rather than just... take that 3rd party puzzle piece and be done with it.
But one way or another, people always complain. Either it's "It needs <Client>" for multiplayer"
, or "It needs me to create an account to play"
. So again - you may thank Steam for that one.
In the end, should it be marked / explained more clearly? Yes, probably. Oh, by the way if it wasn't clear which one this game falls under, it seems that MW5 is using it's own code (crossplay system) and you have to agree to a multiplayer EULA ingame for it to work. At least for GoG. Other platforms also support their native friendlists (the "puzzle pieces).