I'll chime in as a mom whose son does play fortnight. As far as cultural relevancy, there's no escaping that. It's everywhere. The dances especially have crossed into all sorts of other domains. There was a whole segment before the World Series where the players were doing the Fortnight dances. From my POV it's way less graphic than other shooting games. I almost thought it looked silly at first. With the building aspect, it's kind of minecraft meets FP shooter.
Your son's feeling of being left out is pretty appropriate, but your family's conviction about shooting games trumps that. Kids will always feel left out about something. I think the tide is starting to swing away from FN. As to the bigger question of why shooting games are popular, idk. They're fun, you work as a team, there's a decent about of strategy involved, the vast majority of people are mentally healthy enough to separate real killing from videogame killing... I don't have a problem with shooting games, but I really hate graphic ones and don't allow them here. No Call of Duty in our house. Everyone has their line.