Read further in your link...
"The term 'Federal facility' means a building or part thereof owned or leased by the Federal Government, where Federalemployees are regularly present for the purpose of performing their official duties."
Not to sound nit picky, but you're not asking about carrying in a Federal facility, you're asking about gun possession on Federal property.
I don't have a definitive answer, but I'd like to.
I do know that gun possession is not prohibited outright on all Federal property, because I know of exceptions. For example, some military installations have skeet ranges and allow hunting.