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.
It was then that Lord Shiva took the form of Nataraja and performed the famous Tandava or the dance of destruction, eventually crushing Apasmara under His feet. Symbolism Of Nataraja Dancing, in Indian culture has been seen as a way to unite with the Creator.