You likely wouldn't even notice a tail strike like that on takeoff unless it caused a lot of damage. The tail feathers on the exhaust move a bit when you push on them so while they'll have to be replaced, a little scrape probably wouldn't destroy them. If it was a hard hit, the pilot might notice higher than usual temperatures or possibly the engine control unit may notice the problem and show some sort of failure.
It's not exactly common, but it does happen occasionally. F-15 pilots will occasionally scrape the tail on landing if they get too slow in the flare or if they pull the nose up too high while aerobraking. That gets expensive because in the F-15, the parts that scrape are the horizontal stab and a couple of ECM antenna covers. We don't usually do that on takeoff because we almost never do "max performance" takeoffs, but the F-15 can be overly pitch-sensitive on takeoff if the flaps are accidentally left up during takeoff, so that could be one possible scenario causing a tailstrike on takeoff - a jet configured improperly for takeoff.
My guess is that if it's on takeoff, the pilot probably rotated a few knots early, and the burner cans just scraped a bit. At that angle of attack, the wings are creating a lot of lift so there wouldn't be much weight on the burner nozzle. If you look closely, the main landing gear is fully extended and the left main tire sort of looks like it's off the ground, although it's hard to tell because of the shadowing and digital artifacting. It's supposed to be a max-performance takeoff, and that means the nozzles should be getting really close to the ground on rotation. If he's just a few knots too slow however, he might scrape a bit before lifting off.
He probably never knew about it until after landing when the crew chief gave him that sad maintainer look that says "why oh why did you do this sir because it means I have to work late?" Especially since he's #5, nobody airborn is going to be looking at his burner cans during the show so there wouldn't be any reason to call off the demo.