What happens with regard to accident investigation in this context? Is it more important that it was civil, or that it was in a military context presumably doing military transport work?
Considering the governing factors, i don't think this flight qualified as state aircraft under Art. 3 Chicago Convention.
It was a civil registered aircraft, operating under contract of carriage and there was no military personal aboard.
The accident investigation is thus governed by the Chicago Convention. Which means that the afghans have authority with the NTSB being merely observer.
This being Afghanistan of course, applying rule of (international) law is purely academic speaking.