He uses jokin’ Joe the same way - the butt of many jokes (which is not to say they’re undeserved because they’re not, at least in Biden’s case).
He thinks that Joe is "That Guy," and that the world is laughing behind Joe's back, when now, in fact, should Obama (while pointing at and chuckling at and belittling his VP,) turn around, he'd nowadays catch many-and-growing numbers of partygoers laughing at HIM.
Joe is just "That's Joe," but Obama is "That Guy."