The answer to this question can be found in Chapter Fourteen of this great novel. This section comes as Janie and Tea Cake have moved to the Everglades, and Janie is loving her new life and the differences that there are between the Everglades and Eatonville. One of the differences is the general excitement that there is in this new town. To give an example, we are told about a card game, that even when the last card is played, nobody fights or gets angry with each other. Everybody just enjoys themselves. Note what we are told about the card game:
No matter how rough it was, people seldom got mad, because everything was done for a laugh. Everybody loved to hear Ed Dockery, Bootyny, and Sop-de-Bottom in a skin game.
The novel therefore does not tell us the precise name of the card game that was played, except to say it was a "skin game," which presumably is some kind of variant of a card game.