Independence is an amazing ship for teens even if they dont set foot in the teen centre. (In reality Disney's was a few TVs and tables, they just made it look fancier...)
Within the teen centre (living room) theres games consoles and card/board games and crafts all similar to Disney and offer the same kind of activities: trivia, scavenger hunts, paranoia, karaoke, name that tune, boys v girls, teen quest, egg drop...they also have teen rock wall, flowrider, ice skating, free arcade time, and teen dinners in the windjammer. And on busy cruises theres a teen party every night in the teen club, fuel, with a different theme every night.
The ship has a lot of stuff for teens too: flowrider, rockwall, waterslides, skypad, mini golf, arcade, ice skating, laser tag, sports deck.
Theres a whole separate teen compass which lists the activities for the whole cruise. But if no one wants to do them within 15 minutes then they're cancelled and they're free to do what they want.