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.
Given that these Dreamtime stories show the didgeridoo as an essential tool in the creation of the world as well as a device invented directly by the gods, it isn't surprising that the didgeridoo is a sacred instrument. In indigenous Australian culture, the didgeridoo is used in both open and secret religious ceremony.n this story the gods also have bird-forms; Giddabush (a bird also known as the long-tailed fashion) is the didgeridoo player, the Butcher bird plays clapsticks and sings, and the Piwi bird dances. As they play, dance, and sing, they name (and hence create) all of the things in the world.