I put together a guide specifically for parents looking to get their kid started in game development.

That said, it was written for a younger age. 13 is an age where the kid should be more of a self starter, and certainly needs less hand holding. I guess what I mean by that is I recommend the same starting point for a 13 year old that I do for a 31 year old.

Now if you child has shown little interest beyond actual gaming, it could be kind of tricky. If the interest in making games (vastly different than playing them), you really can't change that. However if there is genuine interest, there are a few different routes he could show interest in. Programming, art and design. Depending which he is most interested in, I have different recommendations. For a design, go with a more high level hands on visual tool, be it Construct2, GameMaker, Stencyl or even Unity. For a programmer I'd start with a lower level language combination. My personal recommendation for someone with zero prior coding language is the Lua/Love combination but there are plenty of solid options here. If he is of a more artistic bent, thats pretty much a completely different discipline. As a Student, he has full access to a full suite of applications from Autodesk completely free. Or of course there is the open source Blender.