i think mumblyjoe's hit the nail on the head. you've only had a strat-ish type guitar before (or a guitar with a combined tailpiece and bridge or an acoustic), and aren't used to the bridge being able to come off the body when there's no strings on it. it's supposed to be like that. like mumbly said, the downforce of the strings is what keeps the bridge on, and those holes are for allen keys to adjust the height. without strings, the bridge SHOULD be loose from the guitar. tune-o-matics also come off their posts with no strings on.
it DOES however, look like you are missing only one of the screws that the allen key would adjust...(the one on the left in picture 1) in which case you'd need a new bridge. but before you buy it, look inside the corresponding bridge bushing... it happens 😆