The Tokyo convention of 1963 covers incidents occurring on board aircraft. If the aerobridge was still attached and the door was open then I believe local authorities have jurisdiction, but I’m not a lawyer.
I am a lawyer and I don't know the answer in this case: that's because there is almost certainly more than one correct answer - as LegalApproach alludes to above there are three possible legal jurisdictions which could apply to a criminal offence being committed on this flight:
1. Spain; where the aircraft was parked on the ground when the incident happened; 2. Ireland; where the aircraft is registered and 3. The UK, (actually England and Wales in this case, not Scotland or NI) where the aircraft was heading to (although as I've learnt from this thread, the jurisdiction of England and Wales doesn't 'kick in' until full power is applied on the runway in Barcelona). And that's just the English law. Legal jurisdiction on international flights is a bit of a minefield.
I did watch the whole video and it looks like it was the old lady who insulted the man telling him " he stinks" . Again ,we have a good example of the PC propaganda
In English law, any racist or racial epithet / reference intended to cause harassment/alarm/distress is a more serious offence (and rightly so IMO) - "you stink" is about as mild an insult as you can get, whereas "you black bastard" is a direct reference to this woman's ethnicity. And there is a distinct power dynamic at work when a white man calls a black woman a "black bastard". Even so if she had called him a 'white bastard', which she didn't, the same laws would apply. Call that 'PC' if you want, she should not have told him "you stink"; but quite clearly what he said was more serious and the law (of England and Wales at least) recognises that. However unless the plane had already taken off, that law doesn't apply here.
Thought to ponder: if the victim had called him a WHITE stinky man, does she then get referred to CPS?
If he makes a complaint to the Police of a racially aggravated public order offence, absolutely. Except not in this case, for the jurisdictional reasons above. I don't know the Spanish/Irish law on these matters.