Making someone cry through storytelling (and not onions -lol-) usually comes from the fact that the listener can relate some past memories with the said-story… for example, watching a movie that brings back an emotional past, a book that reminds you of your own experience or maybe a friend's, … a last Christmas dinner with grandma, a lost sister or brother, etc…
So if this is what you really want to achieve then you need to dig into people's emotional past (make an anonymous social survey or poll) then make the game such that "that moment is not violated or trivialised";
I wouldn't advise that the game be replayable because of that moment, instead I'd advise that the game then shows that after such a tearful moment, life can generate joy, hope, happiness and other relivable moments; but the fight to these good fruitful moments is still on: this could be a journey requiring of the player, perseverance, patience, wisdom, discernment and endurance, etc…;
…and the motto of the game could be: “Your life is a not a game, play it wisely” meaning play [the game] wisely, get it? -lol-
have fun ?