Transcript:
Charlie Brown and Patty sit at the table playing a board-game. He takes up the score-pad and asks,"Why did you write 'you and I' on this score-pad?"
He continues,"I thought it was supposed to be 'him and me'" She replies, "It's the same thing, isn't it?"
He puts his hand to his mouth and says,"Well, maybe you're right...I guess I've forgotten"
He concludes,"It's been a long time since I've played this game...."
Original comic:
Best guess is Gin. Looks like a simple 2-player card game, and Gin was popular around then. Not sure what the cup would be for though