The answer really is chaos. Chaos has different definitions used by different authors, but a characteristic they all capture is sensitivity to initial conditions. This requires inherently unstable dynamics (convergence to a fixed point or limit cycle corresponds to an insensitivity to initial conditions) It’s also important to distinguish between microscopic and macroscopic equilibrium. The system shown in this video seems, at least informally, chaotic at the microscopic level (the dynamics of each particle). However, if you consider the dynamics of the distribution (i.e., the ensemble of a very large, ideally infinite) number of balls, it is well known that this distribution converges to an equilibrium distribution known as the Gibbs measure [1].

[1] I’m on my phone and not thinking too hard, you may need to add some Brownian noise to the dynamics for this experiment, but the double-well is commonly used to demonstrate this behavior.