You aren't building your own game if you have a chatbot do it for you.
That's like saying you aren't building a house if you use a hammer to drive nails instead of your hand. AI is just a tool like any other, and you use it to build things like you would any other tool.
"A game" is a different abstraction layer from "a piece of software", though. A game has designed mechanics, a scenario (level design, etc.), art/music assets, writing, and so on. I would say that if you're making all of those things yourself, but you're having an AI write the software that executes the game, then you're still "building a game" per se. "Developing a game" even.
Compare/contrast: people who develop games on top of high-level genre-specific game engines like RPG Maker are still considered to be "building a game." What's the difference between using a pre-made purpose-fit engine like RPG Maker, vs. asking an AI (or, for that matter, a contracted software company) to build you a custom purpose-fit engine?
This is such a horrible cringe and bad faith take.
Eating food doesn't count if you didn't grow it yourself.
Same idea that sends people down needless game engine development / procrastination rabbit holes.
A classic tale from the music production world comes to mind:
"I thought using loops was cheating, so I programmed my own using samples. I then thought using samples was cheating, so I recorded real drums. I then thought that programming it was cheating, so I learned to play drums for real. I then thought using bought drums was cheating, so I learned to make my own. I then thought using premade skins was cheating, so I killed a goat and skinned it. I then thought that that was cheating too, so I grew my own goat from a baby goat. I also think that is cheating, but I’m not sure where to go from here. I haven’t made any music lately, what with the goat farming and all."