I know fights between children happen, but tbh OP it sounds a bit like you know your daughter was in the wrong, from the way you talk and also don't bother looking for witnesses, CCTV, etc...
If the school has an "anti bullying agenda" as you say, wouldn't they have responded to the boy supposedly attacking her? They're definitely not just going off the video – they would've interviewed witnesses, checked CCTV, etc.
If you reversed the roles, and your daughter was doing that to another classmate (whatever he was doing with the stick), who then started "punching and kicking" and "laying into" your daughter, would you let it go?
It's not clear what the boy actually did. There's a big difference between him beating her up with a big stick vs lightly twacking her with a small twig to annoy her, or something in between...
If there's a size difference (though they're only 11 where some girls may still be bigger than boys), even if he was just poking her or something, I do get her rage... But if the video of her attacking him looks that bad, surely she could have stopped after the first few blows? That would've been enough to deter him/defend herself. What if it's a girl her size next and she goes rage mode on that girl again, causing real injuries?
(And I know it's hard to stop once you're physically in rage mode – which is why I don't suggest telling your kids to defend themselves physically. Walk away, report it and know that Dad has your back and will absolutely fight your corner – as you sound like a really supportive parent.)