pretty sure Griff is a big fan of LoF and chose Lexi in his first playthrough
shielding violence from kids is common sense, but we can say that MC and Tink have a warped common sense when it comes to violence given their former career.
also, maybe MC didn't anticipate that Tink would go in so much detail at first when he allowed her to tell the story, while not wanting to have secrets from his girls, but he could still ask her to turn it down a notch.
Kinley didn't react to the violence during the story anyway, so MC probably didn't think about it. he probably would have taken step to prevent further trauma if Kinley showed any reaction.
and violence is everywhere in media anyway, kids nowadays are exposed to it on a daily basis. most are quite a bit desensitized to it.