Hello, you are correct that by default renpy games on Android do not need this permission. That is because they write saves to app-specific folders. Unfortunately, those folders are deleted when the app is uninstalled. Which means that game updates that people play for a couple of days every few months must remain installed otherwise players will lose their progress.
So, some porters have taken to adding additional functionality to write saves in shared space, which is similar to what renpy does on other platforms. This way you can uninstall the game and your saves will remain until you install the next update. In order to provide that, Android requires file access permissions similar to apps that write shared media types like images.
It's also required for renpy games that want to move past the 2GB extended APK data limit (renpy supports only a single extension) or to apply external patches. This is game does not require that but it's the kind of feature that indeed requires those permissions you believe are only suited for File Managers.