Personally, I think most dogs see the door being rattled and then something coming through the letter box as more of a threat than a game , maybe they are in guarding/protective mode . Certainly the 1 dog we owned that shredded mail was of this inclination , he was so determined that even the wire cage didn't stop him so it was lined with plywood but he used to still bite and attack it frantically when the post came through but ignored the box at any other time. Eventually we moved home and the new place had an inner door in the hallway so the problem was solved ......bit drastic though eh ?