It's rather hard to say, as we see only a few clips of the game. However, it seems that the game is some variation of Cheat, where players play cards face down and tell others what card they played. The catch is that they are allowed to lie. The goal is to get rid of all your hand cards.
There are few details to pinpoint a specific variant, but it seems that the cards are played in order (see 7:10 in the episode, where they say numbers 8 to 10 in order).
Also, if your bluff is called and you're found lying or if you call a 'bluff' but the play was true, it seems you're required to add all the cards in the stack to your hand. (See 8:10 from the episode, where Shizuku plays a card, claims it's '13'. Shalnark doubts it but Shizuku reveals it to be a king. Shalnark then picks up all the cards.)
There are no signs of additional rules on how cards are dealt, how they are supposed to be played, if you can play more than one card at a time or if any cards do something special.
Could be that the game is as simple as dealing the whole deck to all players, each playing one card at a time (with Cheat rules), from 1 to 13 (and probably 1 again). This would make a simple game, but the bluffing would be intense.
The manga only shows a single panel of them playing, so that's even less information.