My game can't connect to the server. I can't even request a new password through the game interface. The other two games still work. Could just be a problem on my end though.

My perception of the game's popularity here is based on what is actually being said, not an average review score on a 1-5 scale by an unknown number of voters (not to be confused with written reviews). GOG users often say they don't care about multiplayer, and the game specific criticism on this forum is about the game being hard, lacking active-pause. No one is asking to find players for multiplayer. Also, the dearth of topics overall is an indicator that this isn't a hit with GOGers.

If you want to play multiplayer, you should get Red Dragon which is where most of the community is right now.

GOG is in the business of selling DRM-free games. That means no starforce and other monitoring/copy protection software. What you get is an offline installer that is yours to keep, no validation required after downloading. In the case of Wargame, the multiplayer lobby is hosted by a developer or publisher hosted server. That part is out of both the player's and GOG's control. It is what it is, unless GOG is interested in and manages to get permission to code the game to connect to GOG Galaxy instead.

We can have a "games as service" discussion right now, it's very 2018, or we can retread about a decade worth of forum philosophy on what is and isn't DRM. All the files are DRM-free. You get the entire game. As a product the game is DRM-free. It's the service outside the game that isn't included in the download. GOG notes on the store page that you need the CD-key to access the multiplayer options. They could clarify further that multiplayer connectivity is provided through a third party server beyond their control.

What more do you in the 'this-isn't-drm-free!' crowd want? For GOG to stop selling the game for ideological reasons?

I've reinstalled the game and I can now log in again. The previous post was incorrect, to a point. While it is possible to log in, the chat lobby is greyed out. I can't vouch for the server list functioning either because no one is playing right now, though the interface says 30+ games have been played during the day as of writing. Matches can be public or private, I don't know if both count. I also don't know if the friend interface is working, it says I don't have any friends added which doesn't seem right but memory could evade me (confused with later games in the series?).

Don't get me wrong, the lack of LAN or direct IP connectivity sucks, the game really needs it now that the community it fostered around it's online service has moved on to later games in the series.