Read the decision again. That wasn't what Justice Kennedy said.
The holding of the decision is that any State Statute that limits the definition of marriage to one man and one woman is now VOID (I.e., it no longer has any legal effect).
Since the entire marriage institution sanctioned by Kentucky begins with a definition of the institution as being a state sanctioned union of "one man and one woman", the entire Kentucky marriage code was struck down.
The Supreme Court can void a statute but it can't rewrite it.
At this point (based on everything I know about statutory law and statutory interpretation) there is no such legal institution as marriage in Kentucky.
Legally people might be able to go through the motions of getting married but it has no meaning.
THE SUPREME COURT VOIDED THE ENTIRE INSTITUTION OF MARRIAGE IN KENTUCKY.
Maybe they didn't intend to do it, but the did it anyway.
The law of unintended consequences. Kennedy either didn't bother to realize the implications of his opinion or he didn't give a damn. Personally, I think it was the latter.