The situation is a guy named John. He reads too many books of his preference, but also reads books that other people are reading just to catch up the knowledge they are getting for reading their books. That means he reads books, not only his preferences.
In this context even as a joke could John be called a "third party reader"?
"third party reader" doesn't make any sense in this context. third party means "someone other than the two people who are primarily involved in a situation". You would use it like "Because you and I can't agree, we need a neutral third party to judge our situation", or "When you and I reach an agreement, the opinion of any third party doesn't matter."
But reading is not a situation about two people, and so John can't be considered "someone other than the two people involved".
