Instead of billiard balls being spheres undergoing perfectly elastic collisions, create a new game, probably virtual, in which the collisions are of point particles obeying an inverse square law of repulsion or attraction.
Incidentally, when distances are relatively large and all particles repel, the system behaves like billiard balls.
How should motion stop, providing a static state for the next player's move? The particles never stop exerting force on each other. Easiest is for time to stop (perhaps at a time point controlled by the player), at which point all velocities are set to zero. On the next move, the player gets to set the velocity of the cue particle (ball) and start time moving forward again.
Much more ambitious: simulate electron and position collisions as in a particle accelerator: new particles can be created. The inverse square law only applies at large distances.