Although dated, to me, one of the easiest and most immediately rewarding circuits was a crystal (or diode) radio.
No batteries required, no soldering, impossible to blow up, wiring errors easily fixed, AUDIO OUT, easy to learn how it works, exposure to a LOT of electronic theory, etc..
Except for having to deploy an ample antenna (just a long wire, and more learning experience) it's the "ticket".
Google "Crystal Radio Kits". I know that "HobbyTown USA" has them for $16.00USD (not RS anymore, though).
Good luck getting him off the video game.
73's,
CBB
K4NFF