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 past this ritual was considered a rite of passage for young men. The ritual is directed by a Brahmin priest. Animal Sacrifice is practiced by people in Southern Indian states of Karnataka, Andhra Pradesh, and Tamil Nadu by local Hindu people. It is most notably done in front of Local Deities or Clan Deities.