In this model, the motions of the self-rolling balls are analogous to the motions of gas molecules: both move around in random ways. Pressure in contained gases arises from the force produced when gas molecules collide with the walls of the container.
In general, the pressure on a surface is equal to the total force on the surface divided by the area of that surface. A longer wall experiences more collisions, and thus greater forces, but since it also has a larger area, the ratio of force per area is maintained, and all the walls of an irregular container end up with the same pressure.
Over longer periods of time, the longer walls will be hit about twice as often as the shorter walls. Since each collision applies a force to the wall, the longer walls will have a larger aggregate force applied to them than will the shorter walls. Still, the number of collisions per length of wall is about the same for all the walls, since the longer walls get hit twice as often, and they are also twice as long.
When you place a divider into the arena, creating two uneven sections with a single ball in each section, the divider will slowly move toward the center and eventually reach equilibrium there. The ball in the smaller section hits the divider more often because it has less distance to travel between collisions. Over time, this tends to nudge the divider toward the middle, until the sections are of equal size.
The situation is quite different, however, when one section has two balls and the other section has only one. The two balls will strike the divider twice as often as the single ball, creating a net force on the divider that tends to expand the two-ball section and compress the one-ball section. The two-ball section expands until the number of collisions on each side of the divider is the same, or when the two-ball section is roughly doubled in size.
The expansion of the chamber you witness here is a demonstration of Boyle’s Law: For a gas at a constant temperature, the product of a gas’s pressure and volume remain constant. In other words, if you double the volume occupied by a gas, the pressure drops in half.