Nontransitivity is often quite important in making an effective game. For example, in the role-playing game Dungeons & Dragons, each character is skillful at some things, perhaps fighting, but not so adept at others, like casting spells. The important quality is setting up a varied range of characters where each will be able to beat some monsters but ineffectual when encountering others. A good team has a balance of all traits so that, as with the dice, you can pick the right character to compete in any particular context.
