Why wouldn't it? The SC and this judge ruled the Kentucky marriage law (that she is sworn to uphold, BTW) is unconstitutional, so he is not the legislature and can't pass a law and neither is she, so the is currently no law.
She doesn’t want to sign off on any gay marriages. I don’t see why her office or the state need her signature in order to issue a marriage license. Just put some kind of official stamp on it showing the fees have been paid and paperwork submitted for the official record and be done with it.