Isn't philosophical activity itself just another Wittgensteinian language-game?

I've been thinking about the later Wittgensteinian notion that philosophical activity essentially consists of untangling linguistic knots and correcting the misuse of terms. Specifically, the idea that philosophical problems arise when language,"goes on holiday",when words are taken out of their original, everyday language-games.

Plato, for example. In the theaetetus he tries to find the universal, conceptual essence of "Knowledge," he abstracts the term away from the practical ways we actually use the words "know" or "knowledge" in daily life. Wittgenstein’s therapeutic approach aims to bring these words back to their original home.

But here is my question: Wouldn't this therapeutic, philosophical activity itself constitute its own language-game?

I'm not trying to frame this as a cheap logical contradiction, a paradox, or begging the question against Wittgenstein. I genuinely want to know about the relationship between philosophical activity and language-games.

If doing philosophy means playing a specific game with rules about clarifying usage, identifying nonsense, and giving reminders of everyday use, what happens to the boundary between "observing a language-game" and "playing a language-game"? Is the philosopher standing outside the games looking in, or just playing a very specific meta-game?