Which if you click further around in that section of the NSA website, you'll find that NSA is only talking about information assurance of classified and sensitive military information, not any information handled anywhere in the government.

You have no understanding of how work is dispersed within the U.S. intelligence community.

Which is fine, of course, but why are you trying to speak as if you have authoritative knowledge?

You say that NSA is responsible for cybersecurity within an HR agency because their name has "SECURITY" in it, and as far as I can tell this is meant completely seriously. So should NSA also be responsible for the military defense of the nation since their name has "SECURITY" in it? Should they regulate financial markets because their name has "SECURITY" in it?

In case you wish to know, NSA is responsible for (among other things) 'SIGINT' and 'ELINT'. CIA is responsible for 'HUMINT', 'OSINT', and many other fun things.

Both the NSA and CIA are foreign intelligence agencies, mostly due to historical accident. And of course there's an entirely separate DIA, which also exists mostly due to historical accident, but focuses mainly on military intelligence matters.