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.
The emu belongs to a group of flightless running birds with flat breastbones known as ratites. Ratites are the oldest of modern bird families. They include kiwis, ostriches and cassowaries.The emu's feathers are very primitive and look like a form of coarse hair.tanding up to 2 m tall, adult male emus are Australia's largest birds. In size, they are second only to ostriches in the world. Their powerful legs give them great speed, some running up to 50 km per hour.