Hearing is definitely part of it, but I imagine it's only hearing the sound of the ball being kicked. After that it's going to be far too quiet to hear until it gets close, and he's obviously reacting long before that. Maybe hearing helps him adjust in the last tenth of a second, but he's not hearing the ball's entire flight.

As for the body mechanics of a pitch or a kick, it is amazing. Like, a proper powerful punch involves leg muscles, hip muscles, waist muscles, chest muscles, and only then do you start to get to the arms. For most of us, the best way to realize how coordinated everything has to be is to try to do something with your wrong arm/leg. Everything that flows naturally on your strong side is just completely wrong on your weak side.