I have a Jack Russell who plays fetch with himself too, though he doesn't use the stairs. If the toy is small enough, he can just throw it with his mouth. Terriers are weird.
I have a Yorkie, and this is pretty much standard operating procedure for terriers of any breed. My dood will go so far as to hide the ball underneath a blanket and then leave the room, come back, and hunt for it.
My dog loves to throw things. Especially those rawhide "dingo bones" with the meaty strip in the middle? She throws them up in the air so the meat part will shatter and fall out for easy pickings.
More so. Cats are limited by their inherent laziness; Jack Russell's have the brains and the energy to completely supplant us as the planet's dominant species.