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 hummingbird further deepens this message with its rainbow-iridescent feathers which have caused some species to be named after precious stones, such as the ruby-throated species. People with this power animal, adapt easily to whatever situation they come into, and make the most of their new circumstances.