MTT TL, from your own cite:
The US military continues to use 50 USC 797, citing it in US Army regulation AR 190-11, to support that installation commanders have authority to suspend the 2nd Amendment. The ACT itself does not state this authority, but it is interpreted in the same manner as the suspended portion codified as 50 USC 798.
An Army message known as an ALARACT (ALARACT 333/2011 DTG R 311939Z AUG 11) states "SENIOR COMMANDERS HAVE SPECIFIC AUTHORITY TO REGULATE PRIVATELY OWNED WEAPONS, EXPLOSIVES, AND AMMUNITION ON ARMY INSTALLATIONS." The ALARACT refers to AR 190-11 and public law (SECTION 1062, NATIONAL DEFENSE AUTHORIZATION ACT FOR FISCAL YEAR 2011(PUBLIC LAW 111-383)). This reference is a truncated version of the public law.
The actual wording of the public law restricts commanders to only exercise this authority over military and paid DoD employees while on duty on a military installation.
I put the last bit in boldface, but it's from your source. If you read through your source, it's also interesting to see President Truman's take on the legislation at the time (with which I agree, actually), and the author's point that it was passed during the McCarthy era, over Truman's veto.
Maybe now you see why I ask these kinds of questions.