What do we know about Ishgard? ( Possible Expansion name?)

[Enkidoh]

Doubt it's a church, the sentence is just saying that the leader of the Church (as in - the Pope is the leader of the Church) also serves as the City-State leader. This is not all that surprising since even from 1.0 we know Ishgard has a faith-based society.

Well it is a church-state technically, a form of government known as a theocracy, that is, government by religious belief - a good real-world equivalent to Ishgard would be Vatican City in Italy, the capital of the Roman Catholic Church.