Other than this, demon points are affected by the various events that occur during the game (ex. meeting with Baroa).
Since it's not a visible status, you may think it's useless to think about it, but it's very important for the progress of the game. Also, altough it's hidden, if you pay attention you may hear Cube complaining from time to time about daughter becoming a demon when her demon points increase and come to a critical point (I calculated this happens around every 20-30 points).