No, they don't either in principal (the application in the text is much broader than specifically al-Qaeda -- it includes al-Qaeda, the Taliban, "associated forces that are engaged in hostilities against the United States or its coalition partners", and other who commit a belligerent act against the US or its coalition partners that is seen to be "in aid to" those organizations), nor in practice, because the specific allegations justifying the detention need not be disclosed, nor even the specific detention publicly disclosed, and detentions under the act, while they permit trial by military tribunal, do not require any juridical process or access to counsel to be provided -- that's rather the point of indefinite detention -- there's essentially no practical boundary to their application (if some sympathetic third party becomes aware of the detention, its possible they might be the subject of habeas corpus proceedings, which would require some showing that there was reason to believe that the person was within the fairly broad scope in the text of the act, but that's by no means a certainty in any particular detention.)
You might also look at Obama's signing statement of the NDAA for more evidence for that argument.
No, I'm respodning to you as if you were making an inaccurate fact claim about the NDAA, which you were, whether you refer to what the act says on its face or, even moreso, what the practical result of the authority in the act is.
> I am saying it does not apply here
No, that's not what you said that I responded to. Had you said that, I would not have responded as I did. In any case, theft of secrets in aid of an enemy is a belligerent act, so (even if subsequent investigation ruled out that the acts were done in support of al-Qaeda), were the Administration to, in good faith, believe that the acts were carried out on behalf of or in aid of al-Qaeda, the act here would fall within the ambit of the bare text of the NDAA.
(It wouldn't fall within the requirements of PPD-14, but PPD-14 by its own terms addresses only executive policy on the applicability military custody requirement of Section 1022 of the NDAA, a requirement which applies to a subset of the population for which indefinite detention is authorized by Section 1021 of the NDAA.)
Note I am not saying that the administration treated this as a detention under the NDAA, merely that the concept that the NDAA could -- consistent with the text of the Act -- have been applied here is not at all farfetched.
Again, also, please take a moment to read Obama's NDAA signing statement. He is still the President.