The rules say we must make "...intimate and personal video games based on real lived-in experiences." How closely do our games need to follow our personal experiences? Could we also base it off of the personal experiences of someone close to us (with their permission of course). How far into fiction can our game's story go?

yes of course! although we want a personal experience it can be elaborated on just a small aspect of it rather than telling a complex tale, there are no hard rules as long as it follows this theme and you need to be comfortable sharing this, which may be difficult if it is an exact representation. If you use someone else's experience please do ensure you have permission and ensure that there is nothing to personally identify that person and that it would not make them feel uncomfortable in any way and are consulted the entire time.