He wants to be called a good boy, so the LLM calls him a good boy. Since the LLM is a machine that does what you want, he's essentially doing it to himself. It might not be a conscious choice, but there's still intention behind it. Kein Herr im eigenen Haus. (No master in one's own house.) - Sigmund Freud. He was wrong about a lot of stuff but this is one thing that still stands.
I'm sure you can be unconsciously intent on things, but gaslighting is a unique concept. Here's the definition I am relying on: manipulate (someone) using psychological methods into questioning their own sanity or powers of reasoning.
In your provided example, the user is obviously not trying to manipulate someone into questioning their sanity, nor power of reasoning. Quite the opposite. Lying to themselves (your example) for sure.
