This is not wrong but the term base is click baity but probably an accepted definition from the pentagon. It’s include all facilities no matter or large or small and even those that are part of another base but not on the main campus. It’s almost like a count of buildings.

I haven’t checked, but I would guess this number even includes things like NSA outposts (since NSA is part of DoD) and embassies (which are protected by Marines).

While that may be true, if I understand correctly the typical “base” number is effectively down to a structure. So if you have a radar station in Japan that has a handful of employees and they report up to one of the larger complexes, that counts as a base. It is conflating imo with what people picture as a base.

Generally, intelligence officers/employees (such as people who work at NSA) deploy to bases, or FOBs. I'm sure there are a handful of "NSA outposts" but this isn't generally how it works.

I’m thinking of things like Room 641A. Is that regarded as a base?

No.