This is the "goose drank wine" rhyme as I remember it from my childhood in the 1950's. I don't recall any game or activity associated with it; we just recited it.

Once upon a time
the goose drank wine;
the hen pecked corn
off the streetcar line.
The streetcar broke
the monkey got choked
Steamboat! Steamboat!
Holler like a Nanny Goat!