Sorry, we seem to be at cross purposes here. My fault, as I jumped in and perhaps am misunderstanding your issue.

The GOG version when you buy it has a generic key, yes. You had to contact support for actual keys to replace the generic key, which it seems you did. But those keys aren't actually special in the sense that they're 'multiplayer' keys. They're just actual working keys for the game. If you've replaced the generic GOG key with the keys they sent you and they don't work... then definitely contact support. I've seen reports that some of the keys GOG sends don't work (perhaps an error in them or perhaps they were generated by a keygen, or perhaps something else). Whatever the reason, if your keys don't work, they'll need to be replaced. GOG should be able to resolve it for you.