It’s a tough one, Stepson was/is just the same. Being glued to a screen 24/7 can make kids develop such antipathy to the real world that it can only be insecurity masquerading as boredom/affected world-weariness.
Anything you do with him that involves outdoors with non-gamers will be nothing but torture for his mind and body, and his rolling eyeballs and surliness will in turn torture you.
Buy him a year’s subscription to a good gaming magazine, a box of tissues and a small bedroom-sized fridge for aggressively marketed fizzy caffeine drinks?
Alternatively – a Blu-ray presentation of Blue Planet or something. You never know…it might spark a lifelong hunger to escape pixeljail and become a passionate marine biologist, a penchant for South Sea adventures, and a love for tanned, easygoing Australian photo-journalists. Can I say bush-pilot? What about a flying lesson? Plane has a ‘controller’ and a ‘screen’, almost as good as the sim-thing…you never know, it might set alight a dormant synapse and he’ll become a skilled pilot working for fire and rescue, putting out wildfires, air-sea rescue, cocaine smuggling… endless options with a love for flying.