Moonbase Alpha is similar to Starfleet in many ways, in that it doesn't easily slot into organisations we would have today. Starfleet is based much more on the modern Navy and it's customs of course, and appears way more 'military' while arguing they aren't.
The International Lunar Commission definitely seems to be a civilian oversight committee, and I can see Alpha being regarded similarly to NASA, although I can't imagine a civilian organisation having access to laser-equipped combat Eagles and lunar tanks. Then again, Alpha never seemed to have Hawks assigned to it, and they appeared to be specific combat designs.
Certainly though there was obviously a rigid command structure, it was also very informal. While Koenig was almost universally referred to as Commander by Alpha personnel save Russell and Bergman, (and I assume Gorski was too though perhaps less familiarity with the latter), Kano was rarely called by his first name, Matthias and Carter were referred to by both surname and first name, whereas almost everyone else like Morrow and Benes were called by their first names almost exclusively. It was more department-heads rather than ranks, although the ID pics on the Comlocks have a lot of colour-coded data, which probably actually meant nothing, except that it looked cool.
I suppose then it'd be more accurate to call Bergman Non-Alpha personnel rather than civilian.
