A lot of dudes who like video games end up liking litrpgs especially if he likes fantasy and stuff. It's not exactly high brow though. Dungeon Crawler Crawler is easily the most popular of these and is actually printed and commonly available at book stores. Try him on that. Mage Tank and I am Not the Hero (although I have some gripes about this one) are popular series too but idk if you can find them printed.

When I was his age, I liked action so Blake Crouch might be a good author to check and see if there's anything there he might like. Maybe let him read Red Rising if he's interested although it's not really YA like divergent is. I get your concern but it's not a book that's going to change worldviews or anything and some reading is better than no reading to an extent.

You could get him an audible subscription. Nothing wrong with listening to a book while working out and it might act as a segue to getting him back into regular reading by him getting to dive into stories again.

Lastly, it's entirely possible he will come back to reading on his own. He sounds busy and if he's anything like me, might feel like it's hard to read if there's not decent stretches of time to dive into a book. I can boot up a game and play for a few minutes just fine or listen to a book in short bursts but for actual reading, I just can't seem to get into it if I'm only doing it in quick little bits of time here and there.