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.
So the group Avemetatarsalia is given the name Pan-Birds, indicating its inclusion of birds and all things closer to birds than to anything else. And all modern birds are in the group Neornithes, and are called Crown Birds. But what is the first bird? Well letâs look at our characteristics.