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.
This story is about a giraffe called Gerald who canât dance. At least he canât dance very well. As a result, he gets teased by the other animals. After a devastating encounter at the local 'Jungle Dance', he is laughed out of town. With the guidance of a wise and gentle cricket, Gerald learns to listen to the sounds around him and to his own body, and is able to dance so well that the other animals are left in awe. The message of this lovely rhyming tale is that it is okay to be different and dance to the beat of our own drum.