I understand why your BF feels a bit embarrassed, being beaten up by a 9 year old, but he is being silly. I'm glad he decided to get his wrist checked in the end. Hope he's OK.
Your cousin's behaviour is extremely worrying, and you all need to take it very seriously. If I have understood your post correctly, he hit BF with a heavy object hard enough to knock him off the chair, then stood over him to hit him again with the same object as he lay prone on the floor, and also stamped on him hard enough to break a bone.
I don't think I am exaggerated to say he could quite easily kill someone with this level of violence. Not intentionally I am sure, but a head injury inflicted with a heavy metal scooter could be life threatening.....
As it is, it's ABH, if not GBH.
Talking about "BF being a dick" I think is a real red herring, as it implies there was a degree of justification to cousin's actions.
There wasn't, in any way. If your cousin was perfectly polite in asking BF to move, and BF aggressively refused, that's not ideal, but it doesn't even come close to justifying any element of what happened next. And to be honest, I am a little sceptical about whether cousin WAS perfectly polite. (Tho for all I know he could have been).
And 9 years old is a child, yes, but it's perfectly old enough to comprehend the consequences of your actions......
Cousin needs serious consequences for this, and also urgently needs counselling. Hopefully your aunt realises this, but as a concerned family member who obviously cares about your cousin, please try your best to follow up and ensure both things happen.