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.
Where most birds employ a style of pumping their wings and gliding (so much so that itâs relatively easy to catch a clear look at the wings of nearly any bird at some point during flight), hummingbirds flutter their wings at a speed so high they, well, hum.