There are many good corollaries/commentaries of our Constitution/law enforcement/school system but for my money, the biggest point it makes is what the teacher character (Richard Miller) summarizes at the end. He says that any constitution or law-governing body has to take into account character because we all have a little crime in our hearts. When our own personal constitution fails, we have to resort to a higher one.
Good point, but what hit me (and to me this is the most subtle point the play makes) is that it was a mistake to call this exercise a game. This is underscored many times in the show. It's not obvious, but it's there. Games imply that there are winners and losers. After a while, it didn't matter to anyone that there was a lesson to be learned, they just wanted to win the game. This became so pervasive in the participants it even overwhelmed out narrator in the end.
Here is where I see a relationship with role-playing. We call it a game, but we (the creators/writers all the way down to the smallest DM) de-emphasize the aspect of winning and losing. No one loses the game, not the DM or the players (even though there will be PC deaths) and to win means to get better and rise in level/abilities to live and fight another day. Game means an adversarial relationship and, while there may be enemies and obstacles to overcome in the session, there should be (according to the hobby) no "us vs. them" mentality.
This, I feel, is a big part of the reason the hobby has a hard time reconciling itself with the public at large. Yes, the anti-D&D Christian feelings didn't help but most of the populace see games as a win/lose affair. Without those concepts, while I'm not going to say it'll be hard for Joe Average to understand them, it sure as heck be harder for him to care or invest any time or interest in it. Sports? No problem. Role-Playing? What's the point? That's why there's more Fantasy Baseball/Football players than RP gamers.
Once again, I think it boils down to calling it a game. But, on the other side of the coin, what do you call it (without sounding pretentious)? Event? Happening? Simulation? Damned if I can figure out another name.
To make a long point short, I don't think there is a better word for it. You use paper and pencils (like keeping score in Yahtzee), you sometimes play on a mat (kinda like Monopoly) and a lot of times you have pieces to represent your character (like Sorry!). To the public that equals "game." So be it. Game it is and game it will be.
It doesn't help that the producer of the most recognizable RPG in the world is made by a board game company. But that's just me.