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.
With wings spread wide, the silver brolgas jump, dance, pirouette and prance... Photo: George Pergaminelis. Some birds attract a mate with a beautiful song, some flash their bright feathers and some, like the brolga or the Australian crane, like to do a bit of a dance.ith wings spread wide, the silver brolgas jump, dance, pirouette and prance... Photo: George Pergaminelis. Some birds attract a mate with a beautiful song, some flash their bright feathers and some, like the brolga or the Australian crane, like to do a bit of a dance.