So, Twine creates an HTML5 website, right? Therefore, we can use the Gamepad API: https://developer.mozilla.org/en-US/docs/Web/Guide/API/Gamepad
Since I don't know how to code, all this seems gibberish to me, so... any general tips? I can try and learn how to use it, and if it's easy enough I'll try and make a tutorial or something.
For usage reference (and inspiration) check Depression Quest.