I am really looking for a turned based multiplayer game that still works in multiplayer mode. However, looking for such a thing in your lists is somewhat annoying. There is no way to tell if a game has multiplayer support without opening it, then you get to see if it works correctly..
Maybe add a filter: Multiplayer (for multiplayer without issues), Multiplayer* (for multiplayer that is lan only), Multiplayer** (multiplayer that doesn't work).
Multiplayer issue: multiplayer mode originally built into Original War game is no longer available. For details see: Support
When clicking on the link, you are told, for whatever reason, it doesn't work. Sometimes you are told "...is considered by the developer as a “known issue”, without a solution yet."
What I want to know is, if the multiplayer is not working, can we expect a fix in the future, or should we assume that game is now rendered single player?

At this point you are looking at asking other users for help in getting the game to have a working multiplayer version.
so I think it's good enough to consider it single player only.

I believe it can be safely assumed that the game is single player if multiplayer is currently not working. GOG is more about distributing games and making sure they work on Vista and XP. I don't think they actually look to modify the game itself with their own patches, keeping them the same as any game actually bought in a store or elsewhere.