Yes, because it's not actually area that balances out but mean time between bounce against the black/white boundary.

That's not a stable equilibrium if the hits have a large enough effect with respect to the movement of the balls. The internal circle will create disturbances against both sides of the inner circle, but the outer ball will have to travel a longer distance to move from one side to the other to counter them.

Now the question remains, are there stableish equilibria that are 50/50? Splitting it into two half-circles sounds like an equilibrium at first glance, but I'm not convinced it is, as only a tiny bit of random luck seems to make it become a "horseshoe" pattern instead.

(That assumes that the simulation is randomized of course, which doesn't seem to be the case for the one in the link posted here.)