I hardly think apple or any company are dumb enough to name their backdoor publicly nsagate as a subdomain to their company's domain, it's probably some kind of service, since apple prefixes lots of things with NS (NextStep), it could also be initials for a billion other words, see
http://www.acronymfinder.com/NSA.html
well I guess it doesn't stand for next step a, or they didn't need any more names than 'a' and never went for 'b' ;)
Also it could be "Next Step Administration", "Next Step Access", etc.. there are a billion possibilities, I'm not saying apple doesn't give access to NSA, they surely do, but I'm saying they obviously won't do it this way ;)