What's the purpose of round hole on the stub sticking out of the camera head?

This is one of the camera's optional articulation joints. It is only used for left-handed users if they wish to orient the camera so that the arm is on the right-hand side. You can pop the camera head off its default joint socket on the opposite side of the head (friction fit, no tools required) and mount it on this optional joint socket if you want the arm on the right-hand side.