"Soldiers' POW status recognizes their legal status on the battlefield as duly appointed representatives of their governments."
That part is precisely correct. However, it remains to be seen if it can be enforced, and will be enforced.
Were these people representative of the government of Afghanistan?
What was the government of Afghanistan? Was it the Taliban "authority?" If so, then the people are P.O.W.s.
But if it can be argued successfully, by let us say, the Rumsfeld position, that Afghanistan was in a state of civil war with a government contested, that would leave open the possibility that the people captured are not P.O.W.s, and it is at "the pleasure" of the captors to determine the captives' status.
The captives engaged in acts of piracy, terrorism, and warfare. How they fare depends upon how they acted.