how do you move on from this stupid place? I've walked everywhere and I can't figure out how to leave.

Check your mission (Tab key). It will look something like this:
Receive Intel: Proceed to the Headquarters for mission briefings and intelligence regarding the next operation. (pick up folder on table !)
Choose Loadout: Select and organize your weapons and gear at an armory or designated area before deploying.
Extraction: Leave via the jeep at the entrance.
To be honest, I disable the Malta levels in the menu under Options > Game Options > Story: Cutscenes Only. For an "OG" feel (and a lower difficulty), I set Weapons to "Classic" and Content Packs > Remastered Maps to "No." I prefer the original maps; they are much easier, even with stock weapons.