Rousseau's a writer, so he's obviously pretty concerned with how his audience will interpret his life's work. It's a little weird to end with a close-up of Rousseau reading his book to his buddies, but it's just the cherry on top of a somewhat depressing last few years for the poor guy.
Picture this: Rousseau has finally gotten to the end of over 600 pages of his life. He waits with bated breath for his friends' reactions, only to be met with silence. Mme d'Egmont "trembled visibly but quickly controlled herself, and remained quiet" (12.3.68). That's it? It's a tiny movement, but Rousseau has earned himself the ultimate reward: stirring another human to emotion.