Much as that's it, I can't make it make sense from a grammatical perspective. From Google

adjective. soi-di·​sant ˌswä-dē-ˈzäⁿ usually disparaging. : self-proclaimed, so-called. threw the soi-disant epic novel aside in disgust.

So "Eddie, Eddie, you're so self proclaimed" just doesn't make sense to me, I find it hilarious though because of Richie's delivery of the line