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 name Turkey Trot relating to dancing goes back further to 1895 in the song âPas Ma Laâ where the dancer is urged to go to the Worldâs Fair and do the Turkey Trot dance, so itâs probably a folk dance that became a Ragtime Dance later. The Turkey Trot was not a very graceful dance, but it was considered one of the first of the so called animal dances to catch on with the public. The Trot was basically a face to face dance (meaning not off to the side of each other like the Peabody) taking one step on each beat of the music, while holding her tightly around the waist, or âhuggingâ as it was called back then.