The app used some tricks to get through the App Store review process, which generally prohibits the use of images from Apple products or interfaces. It works just like any other third-party player created for Apple Music and you probably won’t find it in the store as an “iPod Classic simulator”.
That’s because the app comes with normal control buttons by default. The secret is in a function that allows users to add any type of image as a player skin. When you add the iPod Classic theme, which is not included in the app, it hides the buttons so it can be controlled by the virtual Click Wheel.