Interagency coordination. All you're quoting is some non-normative text from some document. It doesn't indicate WHY they say you have to comply with it. The reason is NOT that the FAA has the power to enforce things on the military.
Didn't mean to spark such a fight but there are 2 ways I view this:
1) Driver's License Compact - I can drive my car or motorcycle on my PA Driver's license in any of the 50 states of the US (and some international locations too). While driving in a state other than my own, that state's laws do apply to me and I am expected to follow them. For example, I can be pulled over and ticketed for speeding or not wearing a helmet, even if my state doesn't have a helmet law. In either case, I have a legal obligation within that state to pay the ticket. I can choose not to but the consequences of ignoring it can be dire, especially if I plan to ever return to that state.
What my home state does with the ticket insofar as it effects my DL however is up to my home state. Some states will assign points and take action on out of state violations, others will only do so if the ticket in question aligns with their laws (i.e. I'd get points for speeding but not for not wearing a helmet) and still others will do nothing with them.
In this sense all aviation falls under this category. If I fly to another country (or am in the Military flying within the US), I am bound by the rules of the country I am flying in insofar as they can issue violations and take action against me personally but they cant take my license away. They can forward the violation to the issuing authority sure, and at least in the civil world, most civil authorities will assign a foreign violation to your license just as they would a domestic one but its left to the issuing authority to decide.
Where this example falls short is in identifying the pilot and/or vehicle since there aren't sky-police that can pull you over and ask to see your license and registration. Speeding and other offenses are also often a violation of statutory law, not regulations.
2) Diplomatic immunity - The laws of a country (or state) apply to all individuals within that country regardless of their country of their status/residence/citizenship. The laws still apply to military and diplomatic personnel. A SOFA/VFA often determines how that looks for the military but for diplomatic personnel with diplomatic immunity, the only thing the host country can really do is eject that diplomat, forward the evidence to the sponsoring government and hope that they prosecute the individual under their law.
In either case, the rules of the host nation/state are not entirely binding on the individual. This is how I view it with military aviation. They chose to abide by the FARs but they aren't bound by them insofar as they can change their mind at any time; there is no statutory requirement that they follow them. The FAA is powerless to truly enforce their rules on military pilots, they can only forward the evidence to the military and hope they take action.
Beyond that while, I'm not trying to say the FAR's dont apply to the military (they do because the military chooses to apply them), I have to agree with
@flyingron that citing some nonformative text by written by the FAA saying it applies to the military does not make it so.
As to the training document from the CNAF, the document makes it so insofar as the Military, not the FAA, will enforce those rules and if the next CNAF decides that compliance is not in the best interest of the Navy, then they could just as easily change it.