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.
Roadrunner (The Chaparral Bird)The official state bird of New Mexico is the chaparral bird, commonly called roadrunner, adopted in 1949. More: I was married briefly to a woman from Australia. All she knew about roadrunners was what she had seen in American cartoons shown in Australia. She fully expected roadrunners to be 4 or 5 feet tall.