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.
In the cemetery, the Citipati are supposed to perform a skeleton ritual dance during which they blow the Tibetan long horns. In most monasteries the dance, symbolic of the cycle of life and death, is performed in the monastery cemetery once in summer and once in winter by monks wearing masks. Video