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.
Native American Legends. The Bird Tribes. A Cherokee Legend. Winged creatures of all kinds are classed under the generic term of aninÃ¢'hilidÃ¢'hÃ¯ (flyers). Birds are called, alike in the singular and plural, tsi'skwa, the term being generally held to exclude the domestic fowls introduced by the whites.