If you didn't copy any code directly, this is more a question of trademark (using the Onitama name) and patent (covering the way the board game works) infringement than copyright, if either of those apply. Generally, game mechanic-type patents are difficult to enforce (see nullpomino, which labels itself as an 'action puzzle' game and to my knowledge hasn't encountered legal trouble despite being an exact clone of Tetris mechanics).
So if you don't use the original 'Onitama' name anywhere in the code, I don't think it will be an issue. You can use any FLOSS license on the code, because those generally only cover copyright without respect for trademarks or parents. A notable exception would be the GPL which has a few patent restrictions that I'm not sure would apply to this situation or not.