Vatican City/State is a diplomatic and political site which, for the time being, houses some of the administrative offices of the Catholic Church. The Catholic Church itself is much vaster: it extends across around the world, and from Pentecost until Christ comes again.
Thus, the Vatican state and the Catholic Church can be distinuished. See here (Link)
I think the author’s real problem is with the authority of the pope and his longing for whatever his vision is of “the ideal embodied in Vatican II.”
His closing analogy is quite revealing as well:
>>>>”I understand there is a branch of Judaism that prays daily for the destruction of the Jewish state because it does not conform to the Old Testament model of Israel. Maybe the time has come for Catholics to pray for an end to the Vatican state for the exact same reason.”