You’re overthinking this a bit, the whole point of the matrix is that our reality is fake. Making someone believe they are in the matrix is to make them question their perception of reality. Making someone question their perception of reality is gaslighting.
I know, I’ve seen The Matrix twice, and you’re still using “gaslighting” wrong.
WebMD: “Gaslighting is an emotionally abusive strategy that causes someone to question their feelings, thoughts, and sanity. If someone gaslights you, they’ll attempt to make you question reality. The purpose of gaslighting is to convince you that you can’t trust your thoughts or instincts.”
The definition you found is frustrating because it’s too vague and easily misinterpretable. If you look at any full explanation you’ll see that the “makes them question their perception of reality” in your definition means it like “undermines their perception of reality”.
The way you and the other guy used it is like when mentally healthy people say they have “OCD”. It’s a watered down buzzword version of a term that’s actually useful for understanding life issues when you actually understand what it means.