At the dropzone the pilots usually wear emergency bailout parachutes. But yeah you're right, a skydiving rig would be really uncomfortable to wear flying. It looks like he was planning to jump before he ever took off to me. I've never seen anyone pilot an aircraft wearing a skydiving rig.
I recall now that some aircraft types are modified in a way that the FAA requires the pilots to wear a chute. But as you pointed out, they don't wear a full blown skydiving rig.
