A multiplayer puzzler. Looks fun. I'm not interested in multiplayer though.

What would that equal to anyway?

This brought me a question that I haven't thought before.
Does GoG have any "true" non-local multiplayer games in their catalogue: games that are designed multiplayer mode in mind and that include no singleplayer mode or it is really diminish?

No problem. As you see, this is "a cooperative puzzle game for 1, 2 or 4 players, (...)", whatever it means to play cooperatively as 1 player... ¯\_(ツ)_/¯

Depends on what you count as "no singleplayer mode". I can think of at least a couple multiplayer-focused games that have no real campaign, just matches against bots (Wolfenstein: Enemy Territory and Talisman: Digital Classic Edition).
If you wanna count multiplayer-oriented games that have a "campaign" composed mainly of preset botmatches, there's also the now-delisted Unreal Tournament, and I think Quake III: Arena (though I've only played the Dreamcast port).
I get the feeling that Mobile Forces would fall into one of these categories, too, but I can't say for sure (don't own it). Same deal with Unreal Tournament 2004 (own it, haven't played it...though I get the impression the single-player campaign got more focus than that of the first UT, so this might not qualify); the long-since-delisted (and long dead, AFAIK) free, I think open source FPS Warsow, which was added to new accounts automatically back when I signed up here (and which I also never played); and Screencheat (don't own it, and not even sure it has bots, let alone botmatches).
Honorable mention to Antihero, which has a proper -- albeit fairly brief -- campaign (a large part of which serves as tutorial for the various mechanics), but which does seem slanted toward multiplayer, particularly online play.
And I'm sure there are more.

There are 21 games which GOG hasn't annotated with the "single player" feature, though only 2 that are tagged as online-only.

Those two, Wolfenstein: Enemy Territory and GWENT, are indeed multiplayer-only. A casual glance at most of the others makes me think they'll mostly be false-positives (data quality is not GOG's strong suit), but maybe one or two will be multiplayer-only as well without requiring an internet connection?

I'm pretty familiar wit W:ET and yes it's only multiplayer with no internet also. Of course local LAN games are possible and you can run maps and host local private servers from yor own PC.

= Cube Annihilator

Hence humbly suggesting the subtitle of
Death Squared: Cube Annihilator
// inspired by trailer.

LAN Play, split-screen, how does this work without online multi-player?

Alas, modern games rely on their own servers (client-server model like in MMORPGs) or on Steam (most often).
Almost all games from the second category, when they get here, respectively, lose the ability to play online.

Older games, in which the implementation of multiplayer was still independent (LAN / Direct Connect / etc.), are quite playable even now (regardless of whether they have a single-player campaign or not). For example, Quake 3: Arena.

To answer the question verbatim: there are very few such (both multiplayer and without single-player mode) games in the catalog because there is no point in releasing them here - multiplayer doesn't work in them (almost all modern ones), and in the absence of single-player modes it turns out that it is impossible to play such a game here.

P.S.
GOG team could have solved the problem a long time ago by making their own implementation of multiplayer simulating the network part of Stеаm, as it is done by Stеаm emulators like SmartSteamEmu or Goldberg Emulator (to put it simply - by creating their own analog of such utilities). (It should be noted that in some jurisdictions it is legal to restore disabled functionality of games, so these utilities are legal there)
Unlike these utilities, GOG has no problems with the legal part: they can stipulate it in contracts with publishers/developers.

Unfortunately, GOG lacks either the desire or the necessary competence.

Yes. :-)
I watched the trailer and got the impression, I would have to play all four cubes by myself. For me that seems like it would be more tedious than fun (at least in later levels). But who knows, maybe I'm wrong. I will wait for singleplayer reviews (if there will be any) and see if I'm interested then.

Great local multiplayer game. Very good fun.