You are playing a game on a flat surface during a PT session and everything is going well, but have you thought about the benefits of playing it on the wall instead?
When we actively reach above shoulder level with hands on the wall, the scapular stabilizing muscles (lower trapezius and serratus anterior muscles) hold the scapula in place while other muscles work off that stable foundation to elevate the arm (humerus). Holding in this position dissociates the movement of the scapula from that of the humerus. Dissociation of this kind naturally evolves in babies at about 5-6 months as they are on their stomachs and beginning to bear weight on extended arms. Most children older than a year don’t enjoy a prone position any longer and will protest. Don’t worry, you can get some of the same movement by playing a game on the wall or other vertical surface instead. Check that you have optimal alignment in all other segments of the body: rib cage, low back, hips, knees and ankles.
My favorite motivating games are Tic-Tac-Toe, window washing with a spray bottle and squeegee, drawing with window markers, finger writing in shaving cream, and pulling suction cup balls off of smooth surfaces like mirrors.