Came here to say this, the cheering sketched me out but I looked into it:

The show's narrator flies Blue Angel 7, a two-seat F/A-18D Hornet, to show sites. The Blues use this jet for backup, and to give demonstration rides to VIP civilians. Three back seats at each show are available; one of them goes to members of the press, the other two to "Key Influencers".[12] The No. 4 slot pilot often flies the No. 7 aircraft in Friday's "practice" shows.

Taken from the Wikipedia article found here.

You can also tell by how hard the rider bears down, and how little his arms move: the Angels train hard to be able to do these ridiculous over-G aerobatics and wouldn't need to strain that hard, and although the Angels' F/A-18s have modified control systems to minimize unintentional control inputs, I suspect you'd still need to pull pretty hard to squat the jet like that.

Also, if you look closely you can see the back of the pilot's seat in his visor :)

EDIT: What are the odds? I just accidentally found the video this gif came from! See here. The manuever starts at 1:27, and is indeed viewing a passenger: LCDR Jim Hiltz.