It’s like one of Aesop’s fables, but better in every way.
This story is about one Mt. Kachikachi. The original story actually has nothing to do with a race, and you can look it up if you’re interested. Only the core element, which is a rabbit messing with a tanuki, is really preserved in the show. In any case, this note is about the pun. ‘Kachikachi’ is the sound of fire crackling, and when the rabbit sets the tanuki on fire, the latter asks what the noise is. The rabbit claims that it’s just old Mt. Kachikachi, who they happen to be near to, making noise again. That’s pun number one, the sound of fire. Number two is a complication introduced by Heya, who mashed this up with the Tortoise and the Hare. It now being a race, the players can declare victory, which is ‘kachi’ in Japanese. That’s number two. They were dealt with as ‘catching’ (as in ‘to catch fire’, when Aoi’s banging flint) and ‘catch me’ respectively.