the NSA is a division of the DoD, it is based on a Military Base, and it has many military officers in high ranking positions
if it acts like a duck, talks likes a Duck, calling it s something else does not make it anything other than a duck, this NSA for all practical purpose is part of the military.
They say it is military when they need it to be, and civilian when they need it to be based on what oversight and regulations, and constitutional limits they are trying to get around at any given time
I think "not military" fits pretty well.
Did Snowden "not follow an order" or did he do something explicitly already illegal according to civilian law.
Also note that if captured he's not going to face a court martial, he's going to face the normal civilian legal system.
People in the military aren't "free", by the rules of the military, in the way that private citizens are - the military is a dictatorship, and disobeying is, under their rules, a crime.
I, too, was surprised that this is a thing that can happen.