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.
Dragon dance is a form of traditional dance and performance in Chinese culture. Like the lion dance it is most often seen in festive celebrations. The dance is performed by a team of dancers who manipulate a long flexible figure of a dragon using poles positioned at regular intervals along the length of the dragon. The dance team simulates the imagined movements of this river spirit in a sinuous, undulating manner. The dragon dance is often performed during Chinese New Year. Chinese dragons are a symbol of China, and they are believed to bring good luck to people, therefore the longer the dragon in the dance, the more luck it will bring to the community.