"MA SECDEF" is probably the SECDEF's Military Assistant:
> In the United States Department of Defense, a military assistant is a military officer serving as aide to very senior civilian (typically a presidential appointee in Office of the Secretary of Defense or in the service secretariats)[1]
I'd guess that "MASECDEF QTRS" is that officer's "home phone" (at their living quarters).
Based on the office phones I've used, I'm guessing that the buttons with the 7-digit phone numbers are just used to select phone lines that this phone can make/receive calls on, not speed-dial numbers. I'd also guess that they're on an internal military phone network that's not directly reachable from the regular phone system.
[1] https://en.wikipedia.org/wiki/Military_assistant