Was that an electric crane?
So more pics and one drawing
The arms can more independently to open or close horizontally like chopsticks, and also also pivot together to translate the lifted rocket over to the mount in the case of the booster or onto the top of the booster in the case of Starships themselves.
The lift points in each case are not much bigger than a fist. Booster is a simple downward facing roller pin that sits in tracks, while Starships have a sort of ball and socket arrangement since reentry from orbit doesn't like protrusion. the lift points on each arm cam move in and out on each arm to rotate the lifted rocket about its vertical axis.
The whole point, in addition to catching the rockets, was to do away with transporters like Kennedy, since those are very slow, and do away with overhead cranes that require a lot of hands on rigging time.
The arms ride up and down on those wraparound sections that are lifted and lowered on rails on the tower by the drawworks motor, the last pic. That was salvaged from one of the offshore drilling rigs they bought.