This definition applies to the FA per it's constitution and bylaws.
"All Clubs and Aiffliated Associations shall play and/or administer football in conformity with
these Rules and also:
(a) The Laws of the Game (as deﬁfned in the Articles); and
(b) the statutes and regulations of FIFA and UEFA which are in force from time to time."
[THE RULES OF THE FOOTBALL ASSOCIATION LIMITED, page 1]
Here is a list of references to "association football" on the FA's Website: https://www.google.com/search?q=site%3Athefa.com+%22associat...
"Beach Soccer" is of course relevant because that's the name of the game sanctioned by FIFA.