It looks like he's an LPR for an indeterminate amount of time since the NBC article says "Just days before their trip, she said he received his recently renewed Green Card". At least 10 years but he equally well might've been an LPR back when he originally enlisted. However naturalization under the military provisions should remain as a defense to removal.
Of note are INA 328(e) (8 USC 1439(e)):
Moral character:
"Any such period or periods of service under honorable conditions, and good moral character, attachment to the principles of the Constitution of the United States, and favorable disposition toward the good order and happiness of the United States, during such service, shall be proved by duly authenticated copies of the records of the executive departments having custody of the records of such service, and such authenticated copies of records shall be accepted in lieu of compliance with the provisions of section 1427(a) of this title", which points to:
INA 316(a)(3) (8 USC 1427(a)(3)):
"during all the periods referred to in this subsection has been and still is a person of good moral character, attached to the principles of the Constitution of the United States, and well disposed to the good order and happiness of the United States."
INA 318 (8 USC 1429) Prerequisite to naturalization; burden of proof:
Except as otherwise provided in this subchapter, no person shall be naturalized unless he has been lawfully admitted to the United States for permanent residence in accordance with all applicable provisions of this chapter. The burden of proof shall be upon such person to show that he entered the United States lawfully, and the time, place, and manner of such entry into the United States, but in presenting such proof he shall be entitled to the production of his immigrant visa, if any, or of other entry document, if any, and of any other documents and records, not considered by the Attorney General to be confidential, pertaining to such entry, in the custody of the Service. Notwithstanding the provisions of section 405(b),1 and except as provided in sections 1439 and 1440 of this title no person shall be naturalized against whom there is outstanding a final finding of deportability pursuant to a warrant of arrest issued under the provisions of this chapter or any other Act; and no application for naturalization shall be considered by the Attorney General if there is pending against the applicant a removal proceeding pursuant to a warrant of arrest issued under the provisions of this chapter or any other Act: Provided, That the findings of the Attorney General in terminating removal proceedings or in canceling the removal of an alien pursuant to the provisions of this chapter, shall not be deemed binding in any way upon the Attorney General with respect to the question of whether such person has established his eligibility for naturalization as required by this subchapter."
Sections 1439 and 1440 are INA 328 and 329.
Then finally USCIS Policy Manual Volume 12, Part I, Chapter 3, A:
"The applicant must demonstrate good moral character for at least 1 year prior to filing the application until the time of his or her naturalization."
So it's kinda on him for not seeking naturalization while in active service, and not seeking it after meeting 1 year of good moral character following the drug conviction, timing would depend on when he completed his probation but I doubt he'd be in probation that long, he could likely still argue that INA 328(e) exempts him from the normal good moral character requirements.