This is the worst argument about the powers of the state I have ever read on any forum. Ever. It is not where any Christian conservative would start his argument, nor a libertarian conservative either.
Somehow, I think that marriage eminates from something far more original and primitive than with the chief of police of the State of Connecticut.
You misunderstand the sentence. A state must have some power before it passes a law, a power that gives it the right to pass the law. The states have the police power, and contract law is based on that power. It has nothing to do with religious belief, it has to do with the state constitutional power to pass laws.