Basically, it's a game of "duck, duck, goose" - but with cocks. (To wit: one fellow going 'round the circle, tapping heads and saying "duck, duck, etc...until a 'goose' is chosen). After the "goose" is chosen, that fellow chases the protaginist around the circle. If he is caught before he has a chance to sit in the newly vacated spot, he then performs oral sex on the "goose", much to the delight of the other players. If he is not caught, the game progresses until somebody gets a blow job. That's...pretty much the point.
"Golly gee, THAT was The Kankakee Goosechase at the bathhouse last weekend? It took me forever to realize that I needed to slow down to get to blow someone!"