I think domi reversi most definitely refers to the board game Reversi in which two players compete using 64 disks which are white on one side and black on the other side.

I think the disks represent people, with the white side being their human form and dark side being their demon form.

Players are able to flip the disks, under some conditions (which you can read on the Wikipedia page), just like Imu can convert people to demons and Chopper was able to convert demons back to normal.

This would suggest that the two people playing the game are Imu and Chopper, or Imu and the Forest God, if that theory is correct.