I remembered there were third-party games available on the iPod, but checking https://en.wikipedia.org/wiki/IPod_game , it doesn't look like an SDK ever made it to the public.
I would imagine the "OS" doesn't have a lot of graphical routines, just to draw text/menues, scroll bar (to indicate song progress) and some library to display images (for album covers). And that it boots straight into this player app, and it has no idea of how to load other apps...