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.
âHis aerie of rare birds was haunting and a very clever visual.â âFrom 1960 to 1962, Kretschmar and Leonovich found that 19 of 23 Peregrine Falcon eyries in the Pyasina basin were associated with Red-breasted Geese, as were 11 of 12 eyries on the Pura River in 1996.â