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.
One of the most spectacular sights on the Galapagos is their courtship dance, when they bow and sway, honk and whistle, point to the sky and fence with their long, yellow bills. Various species of petrel are common on many of the islands, of the archipelago but the dark-rumped petrel has been in danger of extinction.