I'm going to quote from a post I've made on a similar topic (also includes a link to another related post):

Culin lumps all these all into his category of games influenced by or adopted from Europeans, though the ethnohistorical sources indicate that several of these games had "been long known" to their Native players and were played with rules that were unfamiliar to Europeans. If they were picked up from Europeans, these games quickly evolved into new creatures. I'll mention two board games developed by Eastern Woodland cultures here.

Musinaykahwhanmetowaywin is an asymmetrical game played by the Ojibwe and Cree. The board is a cross-shaped pattern of five squares, each of which is crisscrossed by four lines (vertically, horizontally, and diagonally). At each intersection is a slot of one of the fourteen peg-pieces. Thirteen of these pieces are small human-shaped pawns; the last is a much larger ogimaa piece (to update the spelling used in Culin's book. Unfortunately, I don't know enough Ojibwe to even begin to figure out what the game's name should be in modern orthography). One player controls the pawns, while the other controls the ogimaa. On it's turn the ogimaa can move in a straight line as it pleases, capturing pawns as it goes (though there does seem to be a way for the pawn-player to protect his pieces, the specifics there aren't mentioned). The pawns can't capture the ogimaa directly. Instead, they have to herd it into a position where it can't move away.

Ko-ko-nag'n is a Passamaquoddy board game that has been compared to checkers (a game that was adopted from Europeans and widely popular among the members of the Wabanaki Confederacy). We don't know much about this game except that it was regarded as particularly challenging (Euroamerican writers never seemed to have picked up the rules and only a few Native players were said to have been any good at it), circular and square pieces of differing values were employed, and unlike most games, men and women could play against one another.