Coming in late on this one, but here's the advice I've given my (not quite 13) oldest son:
Your mileage will vary with any "gaming" degree. A solid background in computer sciences will go a lot further. Cut his teeth on an introductory gaming ecosystem like Gamemaker and walk through as many tutorials as he can. Play around with the variables in those tutorials, make mistakes, break things, track down the bugs and fix them. I learned more at an early age from typing in umpteen lines of Basic and machine language code from old Compute!, Ahoy and Compute!s Gazette magazines than I ever could have planned for.
Play board games. Lots of board games. Try to break them down, figure out why some take longer than others, why some bring people together (Zombies!) and others pull teammates apart (Risk). Same goes for D&D, a good DM can teach a lot about competent scenario building, and a shitty DM can teach even more if you're paying attention.
Get a CompSci degree above all else. Even if he doesn't use it much going forward, it will help a lot when engaging in cross-discipline communication with coders, and that makes all the difference. I'm self-taught, but I want to go back when I have time and get that degree under my belt as well...