The area is "closed" (not open), or "restricted" to alcohol consumption. Here is a memo reminding of alcohol restrictions, noting 36 CFR 2.35 which states that
The superintendent may close all or a portion of a public use area or
public facility within a park area to the consumption of alcoholic
beverages and/or to the possession of a bottle, can or other
receptacle containing an alcoholic beverage that is open, or that has
been opened, or whose seal is broken or the contents of which have
been partially removed.
This was done in the case of the area, apparently a few years earlier (i,e, it used to be allowed and there was a policy change). The Gateway Nt'l Park website states that "Alcoholic beverages at Sandy Hook are prohibited", as are a bunch of other things.
The motivation is part of the regulation, that the superintendent determined that
(A) The consumption of an alcoholic beverage or the possession of an
open container of an alcoholic beverage would be inappropriate
considering other uses of the location and the purpose for which it is
maintained or established; or
(B) Incidents of aberrant behavior related to the consumption of
alcoholic beverages are of such magnitude that the diligent
application of the authorities in this section and §§ 1.5 and 2.34 of
this chapter, over a reasonable time period, does not alleviate the
problem.
