No complexity involved, move the beads in a manner that suits you. A bead spinning and flipping joy.
The Play/Pause AppleTV button on the Siri remote will allow changing to the different cube beads.
This game will show a virtual bead that the user can fiddle with single finger gestures. There is no demand to move fast or slow, so the APP could be used to burn off excess energy or stress. The APP could also be used as a dexterity test, where someone would make requested changes to all the beads within a certain time.