Final answer:
The term for a free-for-all fight associated with Irish fair rioting is 'Brawl'. It denotes a noisy or disorderly fight, which fits the context of a riot at an Irish fair.
Step-by-step explanation:
The name for a free-for-all fight that comes from the Irish fair known for its rioting is B) Brawl. This term was historically used to describe a rough or noisy fight or quarrel, and it originated from such events where disorderly and chaotic fights would break out.
While 'melee' generally describes a confused fight or skirmish involving several people, 'fisticuffs' refers to fighting with the fists, and 'skirmish' means a small or brief fight, brawl is the word that specifically links to the Irish fair riots, making it the most suitable answer.