Whether they have any extant function or not, they have lost their former function and in that sense they do fit the definition of vestigiality. Vestigial structures are often called vestigial organs, although many of them are not actually organs.
There are quite a few birds famous for doing ritualized mating dances, so I would only list 5: The Red Capped Manakin, The Black-footed albatross, The Western and Clark's grebe, The Superb bird of Paradise, & The Victoria's riflebird.
Perhaps the most renowned Highland Dance is the Sword Dance, which has its roots in Scotlandâs embattled past. Some suggest that Malcolm Canmore, King of Scotland, who ruled the country between 1054 and 1096, created the dance. In 1054 Malcolm Canmore began the military campaign that Macbeth made famous.