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.
Bill Robinson & Shirley Temple. By the time that Bill Robinson (1878 to 1949) became famous as Bojangles, tap dance shoes were part of the total package. Robinson wore tap shoes with wooden soles and heels.