They are not a church. But that shouldn’t matter. He’s a real minister, who has the right to refuse performing a sacred rite to anyone outside his faith tradition.
Real hard to make the case it's a "Sacred Rite" when these ministers seem to be running a resort-town wedding chapel with no religious affiliation.
I was married in a similar chapel in a similar location and I'm not going to tell anyone it was a religious ceremony, although religious elements were mentioned.