True but I don't think the distinction matters to the overall point that it's perfectly ordinary for religious institutions to operate a TLD, regardless of the mechanism that allows for it.
Vatican City is a theocracy, not a religion. You'd technically have to add .uk and many more to the list if you're broadening to all nations with a state religion.
It's the central bureaucratic/theocratic function of a major world religion which, it just so happens, is organized as a micronation instead of as a foundation or something like that. The primary function of the UK is not to run the Anglican church, nor is their king generally thought of as their primary leader.
