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.
Griotic Dance . A griot is an African bard, a tribal historian and storyteller. Griotic dances are story-dances, the oral history of a people set to movement and music. The Lamba or Lamban was danced only by the tribe's djeli or griot. Today, African dance troupes perform the exuberant, once-exclusive moves.