I didn't pay any attention to this at all the first time I watched the episode. While the game is sort of important in the episode, it's more important for what it causes than for what it is.
In any case, I'm pretty sure the name is a subtle reference to the Black Forest in Germany (der Schwarzwald in German). German culture informs a lot of the stories that the show adapts (like the Grimm fairy tales, which resulted in the show's name) and the history in the show itself. In one episode, I think Monroe even mentions some ancestor of his who lived in the Black Forest.
