This is the first time I've seen it! Earlier, after I saw it, I looked online for info about it and found this article online that says:

In the Grey [squirrel], Laidler describes solitary play as consisting of tumbling, acrobatics and creeping along or around an object, sometimes rubbing the body against it at the same time. Play fighting with an object is also frequently observed, involving the squirrel lying on its back and manipulating the item with its paws, frequently scratching and kicking it. In the case of Red squirrels, as well as play chases involving several kittens, the late Max Planck Institute behaviourist Irenäus Eibl-Eibesfeldt described solitary youngsters kicking away a stick before pouncing on it again to resume play.

I have observed object-play behaviour in both young Red and Grey squirrels and seen videos of adult Greys engaging in solitary object-play; in each case a stick/twig was the toy.