If Sburb is a game. How do you think it would handle things like pausing and saving? Would those features be exclusive only to time players?

Likely only to Time Players, although Pausing is really just someone ZA WARUDOing the Session. It uses Game mechanics and parodies Game stuff, but do remember it’s not just SBURB, the entirety of the Homestuck-verse sorta acts under Game Logic a lot of the time.