It is totally incorrect to say every time a court strikes down a state or federal law then the entire law ceases to exist.
Sometimes, a court will, in fact, throw the whole thing out. Sometimes it may strike down only part.
In this case, SCOTUS voided all laws and state constitutional amendments as they apply to prohibiting gay marriage. It did not throw overboard all states' entire laws that apply to all marriages.
Don't you think Davis's attorneys would be making that case if it had any basis in reality?
Did you read the KY law at the link I provided? The issue is quite clearly addressed and deeply intertwined. Rather difficult to extract the objected-to parts without voiding the whole thing.
One way or another the law MUST be formally re-written or struck down entirely. The nature of law is NOT to just ignore bits of it based on vague statements, even if those vague statements are compulsory. We have to know exactly what the law is, SCOTUS ruling having been applied.
Having read the statutes that define when a clerk issues marriage licenses, they all are worded gender-specifically, and all rely on the explicit definition of marriage as man & woman.
They all were voided because they all are foundationally related to hetero marriage.