In Territorial Die-Spute, you (the player on the bottom half of the screen) win by defeating the AI opponent (on the top half), using physical die (by pressing the Space key). The green die can restore or damage your HP, the red die determines how many times you attack in that roll, and the black die can influence a particular stat.

The red attack die also takes any neutral tile it lands on, and makes any taken tile it lands on neutral if owned by an opponent.

Edit: There is a bug with the gameplay UI not appearing correctly when the game is not in Fullscreen. I would reccomend playing the game in Fullscreen for the best experience with the game.