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.
Dancing their way across the country, one of our largest and most elegant birds is on the move. The curious dance of the Brolga is legendary, but we really know very little about this majestic creature. June is the month when Brolgas in Australia's south are making their way to the breeding grounds.In the north they're heading out with their new chicks to join massive flocks where new mates pair up for life.he curious dance of the Brolga is legendary, but we really know very little about this majestic creature. June is the month when Brolgas in Australia's south are making their way to the breeding grounds.