The bottom line here is that this woman's religion disqualifies her from holding public office. She doesn't not belong to a government approved religion. If she did, she wouldn't believe what the government says she should believe so that she can keep her job.
Ideally, the government would have stayed implementation of anything until a new law could have been written that did not require someone to violate their religious beliefs.
As it is, because they have forced this forward, they have no active marriage law under which to marry anyone or to punish anyone.
You are right. From what I read, she had to sign off on all licenses so she couldn’t just let someone else do it, so I don’t know what the solution is since the central gov’t nullified the state’s laws.