Thought the hex might be meant to hold bits, but now that I see it on a big screen, it looks like it has a key on one side.
Not sure it's much help, but mine looks nothing like that inside:
The screw is a left-hand thread and a much larger diameter than that tiny hole at the bottom of yours:
Model # of mine:
My older one is the same:
Think mine is taper-fit, so it
needs the screw. Yours looks like a pressed-on hex with a key, which doesn't necessarily require any kind of screw. If you can find one that fits and a washer, you can use it to press it back in...if not, well, not sure if hitting it with a hammer hard enough to get it back on wouldn't break things inside.