That's pretty standard for bullying, actually. The bully only does the really bad stuff where teachers can't see, then provokes the bullied into lashing out at them in public through small annoyances, then claims to be the bullied.
When it's caught on camera like this, though, it's blatantly obvious that the little kid was the instigator and real bully, so the administrators punishing the big kid for finally doing what he needed to are just idiots.