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.
History of Chicken Dance Day. âDer Ententanzâ was the name of the song that inspired all of this, and while the dance has come to be called âThe Chicken Danceâ, the song itself is called The Duck Dance.