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.
Not all birds are instinctive flyers, however. Flightless birds, such as penguins and ostriches, no longer have the instinct to imitate their airborne cousins. Newborns of bird species that do fly, such as pigeons or hummingbirds, have an innate sense that it is a natural act.lightless birds, such as penguins and ostriches, no longer have the instinct to imitate their airborne cousins. Newborns of bird species that do fly, such as pigeons or hummingbirds, have an innate sense that it is a natural act.