Killing one person is murder, killing 100,000 is foreign policy
The governor doesn't control Federal Court contempt charges.
An amended complaint has already been filed and a hearing is scheduled concerning Judge Don Davis refusal to issue licenses for Thursday at 1:00PM. The outcome of that hearing will either be a dismissal or injunction against Davis (probably in the form of a writ of mandamus). Then if Judge Davis doesn't comply he'd be subject to Federal contempt charges.
The decision is non binding because it is a district court case. It is not even binding within the same district much less the entire state. The only thing "binding" (for lack of a better word) is the order directed at the defendant, which is the Attorney General with no power over issuing marriage licenses.