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.
The Dragon Dance originated in China during the Han Dynasty(180-230AD) as part of the farming culture. The Dragon is an amphibian, able to move on land, able to fly in the sky and able to swim in the sea. As the dragon gives people a feeling of great respect, it is often called the Sacred Dragon.