Pointer to instance is not retrieved and passed when calling static function.
Well, some wrapper functions are here, right. But only a few.
All those functions can be simple static function, but using them as member of inner class we have access to private members of outer class. They are not used intensively now, but there are space for simple extending.
Other good reason to have all this kitchen in inner class is to have all in one place. You don't need to look at whole code to find where is variable/function is declared.
And we hide all those functions from public API.