I know what program you're talking about. (I saw it, too, and that line confused me for a moment, too.) However, I know that Charades has been called "the game" in some circles, at some points in the past, and sometimes has been played with different rules. When she said "This isn't Charades, it's the game," she was giving him the name that she and her family use for it. If you've watched the show, you know that he comes from a different background and social class from the others at the party. I believe that this exchange was meant to emphasize that he was different. I hope that helps!

Like Eliot said although I think it is the other way round, I think she is saying this isn't the charades I normally play (the real thing), it's just the game.

Charades = a readily perceived pretense; a travesty There is a game called "charades", but it is a different kind of charade. The whole thing here is a pun. The woman means: "This is not pretense, this is the real thing."

I would need to see the show, but what she probably means is that she takes charades very seriously, or that game is much more important to her than other games. You might say about your girl/boyfriend. She is not just a girl. She is THE girl. If you really like pizza, you could say, "It's not just food, it's pizza." (letting people know that you REALLY like pizza.)