“The parent/parents have the responsibility to monitor their own children’s behavior but I believe the game also had some influence.”
My 13-year old son once a week plays a teen video game (WW II first shooter type thing). I’ve watched it a bit and it looks pretty fun and not too graphic. However, one time he did come home from playing it and said something mean and “shot” his 10-year old sister with his finger. He got to skip the next week’s time to play it (at a friend’s house) - and has been good about it since. Same thing with PG-13 movies - if he gets caught using a swear word - that’s it.
That’s kind of how we do it here. Playing some of these games is a privilege and can be quickly yanked. Consistency is the key for us.