If you are still oblivious to the game they play, then I'll give you a big hint - it start...

Monopoly? : ^ )

Nope. Just think about this whole set up, it's right before your eyes. But you are close! It is a party game.

(It might not be under the same name in different parts of the world, but origin of the idea is the same)

I got nothing, any more hints?

Not to beat around the bush, here it is (spoiler ahead)...
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the game - https://icebreakerideas.com/mafia-game/
(A bit more in depth about it if you are curious https://en.wikipedia.org/wiki/Mafia_(party_game) )
The set up, the number of players, roles - fits in perfectly. The only difference is how it actually plays out, but that's actually how every game session is different in it's own way. So far each game in Borderlands had a similar counterparts.

So it was Mafia! That was the only M game I could think of, but it just didn't fit in my head, I've never played and the werewolf game is usually portrayed as pick card, murder at night, need to find 2 werewolves. I kind of still don't see it, damn my literal mind.

You must understand that 'game' is just a stage for an actuall struggle for life. Remember how in the Imawa no Kuni at the final game they played Croquet, that had nothing to do with croquet as a winning basis, an actual fight happened with their minds(not to mention the drug Mira used).
I may not be spot on, but so far nothing else matches with the known games, so it can't be anything else then that type of game, in a sense that it's just a premise. Just like the world they have to stay in.

So far I think not every character in the manga can be what they appear to be, even after those shoking revelations they might still be keeping their masks on. Like Kimari might actually be on 'Detective' role, accepting the guilt for murders to keep his actual identity from 'Mafia' the actual murderer, as one who's able to detect him, to expose and defeat him later. Or I might be overthinking it and the 'final' cat is out of the bag. But it feels way too simple...

As for the Croquet game at the end of series 1, I think it was a direct allusion to Alice in Wonderland, as the Queen of Hearts was always playing Croquet to pass the time

Indeed. But author picked the Alice in Wonderland theme for that specific reason that it is not about 'games' but Life and Death border state. So like in each work croquet had little point as an actual game with rules, but rather a stage to tell a story about "worth of life" and what it is. And the whole story is constructed in a smart way, each part connected, sometimes having more then one meaning.