Taliban fighters and operatives do not meet the criteria set by the Third Geneva Convention.
They do not act in a manner meriting protection as a non-signatory of the Convention in Article 2, nor does Afghanistan of 2001 meet the standards of a sovereign nation capable of entering into international treaties.
They do not identify themselves or function in a manner that meets the requirements of Article 4.
Even if called a "resistance movement" their terrorist nature does not meet the requirements of Article 4.1.6.
Therefore, they do not earn the protection of Article 5, and it is highly possible that the mass graves mentioned in this article are filled with those who have justly received death sentences for terrorist activity as per Article 3.
As for protections under the Fourth Geneva Convention, sorry Charlie, but the Fourth is about the protection of civilians in armed conflict. Taliban fighters and operatives are not civilians.
It does not surprise me that the New York Times, an institution that cannot tell the difference between journalism and being a voluntary agent for political activism, also cannot tell the difference between soldiers, terrorists, and civilians.