There's a game in this video, more-or-less the same tune. Looks like they're passing shoes around in kind of a "musical chairs" arrangement. The players are a little older in this video - are they passing around packs of cigarettes?

Looks like fun.

Seems like it's usually spelled "Ziggy Ziggy Za," but the Astrud Gilberto recording is "Zigy Zigy Za."

-Joe-