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.
Dance dramas of Java and Bali feature episodes from the Hindu epics, Ramayana and Mahabharata. Some famous dances are ... Legong (pronounced LAY-gong) is a graceful Balinese dance performed usually by young girls dressed in gold brocade wrapped tightly around their bodies and headresses decorated with flowers.