The game from The Beast From The East seems incredibly bizarre and nonsensical at first read, but then consider what kind of creatures the Beasts are. A lot of the rules seem to involve feats of great resilience (getting bitten by snakes, eating insects) or resourcefulness (always tagging from the east, finding ways to trick other players). In the end, they let the kids go after it seems like they've "duplicated" themselves. Therefore, it could be the Beasts are Social Darwinists, and judge who lives or dies by strength and intelligence.
The Beasts assuming the children are familiar with the game when they clearly aren't makes more sense when you realize they likely have encountered humans before. If we presume humans have been stumbling upon for this world for years, the Beasts would believe it's commonplace. The survivors of these games either wouldn't be believed for telling crazy stories, or would try to forget the trauma of the Beasts' forest.
The Beasts are cannibals. Since they presumably don't always have unsuspecting lost children to play with, and since someone has to be the loser of each game, we can assume they eat each other.
