How old is he? It is fine that he is inside-only for now, he's probably safer that way, but maybe if you got him used to a leash and harness, he'd be happy with "walks" outside, rather than someone having to open a door or window for his perusing pleasure.

How old is he?

Definitely pick up some toys, and teach your mother how to use them to play with him. He sounds bored more than anything. Does he have a cat tree near a window? That might help, so he can look outside and watch the world, but stay safely indoors, and not be begging at doors!