I would say that the author is refering to the Catholic Church pre-1054. While the falling out began prior to that, certainly one would say that in the early centuries of the Church, the East West divide was not nearly as pronouced as it has sadly become today. Would you agree?
Up until the 1054 the church was fairly unified. I just don't like the way the article uses the generic term primacy, as though everyone in 1053 had the same definition as the Vatican I definition.
I think a return to the pre-1054 understanding of primacy would be a huge step toward ending the schism (that and a real effort on both sides to stop picking converts out of the other's parishes).
Further I think the combined weight of both churches could do a lot to eliminate protestantism.