No cats here but I have 2 small dogs, a Pug and a Boston Terrier/French Bulldog cross.
The pug can open the door similar to your cat crazed, he will just scratch at the corner if it is slightly ajar until it pops open enough for him to wedge his head inbetween and push it open. The Boston is just crazy, can't open doors but he can run circles around you all day and not get tired lol.