You quoted me talking about Construct's File Chooser object, which is a different kind of object that the 'Taking screenshots' example does not use. (I'd note you haven't provided a link to the context, and the date is 5 years ago so it could well be out-of-date and no longer applicable anyway.) The File Chooser object is a button that you can click to choose a file, but it provides read-only access to that file - it cannot write a file to storage. As far as I'm aware File Chooser does work fine on Android, but it doesn't help you save files.
You could also try saving data with the Local Storage plugin instead. It doesn't save to a file, but it still saves it permanently allowing the app to later recall it. Other than that, perhaps there is a third-party plugin that may help.