,Angie-chan, thanks for sharing information about that game song! These old songs may have been regional. I'm African American and lived in New Jersey as a child and I never heard of "Way down yonder in the brickyard" or the "step it down movement". Furthermore, we didn't do any parallel line children's games when I was growing up, and only became acquainted with that concept through the 1971 to 2006 R&B dance show Soul Train with its "Soul Train line" of females and males facing each other and one person or two people taking turns dancing or struttin' down the middle aisle.

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A glimpse of a children's line game is found in "Pizza Pizza Daddy-O", a 1967 Bess Lomax-Hawes film of African American school girls in Los Angeles:
http://www.youtube.com/watch?v=N2YodFqZ7nQ

And here's a link to a YouTube video of a Soul Train line:

a href="http://www.youtube.com/watch?v=C18CTFrI-tU">http://www.youtube.com/watch?v=C18CTFrI-tU