What is aerodynamic damping?
The link you provided has a poor choice of words: "restoring moment".

Damping forces are not restorative, i.e. they do not attempt to return the body to equilibrium, but rather oppose its movement. That is an important nuance.

Imagine a classic spring and dashpot vehicle suspension: the spring tries to restore the vehicle to its regular position, while the dashpot damps the velocity. By itself, the dampener will not restore equilibrium, it will stay at whatever position you extend it to, despite fighting the movement itself.

How does this apply to your question: aerodynamic damping is exactly that, the opposition  of the aircraft to rotation. You can observe it without flying: just imagine an aircraft hanging by its nose and tail, in such a manner that its CG is right between the supports. You can roll it by hand, but the drag on the wing will eventually stop this roll, but it will not level out the wings.

In flight, there are other forces at play that do provide a restoring moment, but aerodynamic damping does just what it says on the tin, it damps.