But I will talk to him (not his parents) about design not being an entry level position. If I can get him to imagine himself in a skill-oriented, content-creation-focused discipline (say, BFA in Game Art) instead of a more administrative role, I think I've won the hard battle. That would entail him being interested in obtaining a skill set, confronting his fear of failure, and provide a clear way for me to train him to develop better work/self-study habits. After that, convincing him that a traditional art foundation is the superior path is almost a foregone conclusion.
You are teaching him programming and math (great!), he wants to get into game design, so you want him to major in art? That doesn't sound quite correct to me... but I'm not in the industry. How'd art even get into the picture? Has he already shown interest (and natural skill) in art? If he has skill for programming, wouldn't a computer science degree be more appropriate?
He was looking at design for the wrong reason. It was because he was afraid of failure (and in art/coding it is very clear when you don't know what you're doing). He saw game design as a less intimidating alternative because of the murkier metrics of individual skill. I openly accused him of this Friday and he said "wow, you really hit the nail on the head!"
I still want him to achieve his desire to be a game designer. I do not think that going to school for game design is a good way to achieve that (I am not in industry either, just repeating what I've distilled from what I've read). I think that having a strong marketable skill, a useful trade which allows you to get your foot in the door / prove yourself, and then branching into a more executive role is the way to do it. And the best way to do digital art, is to know how to do art. The actual tools you use are fairly easy to pick up; they are not the limiting factor.
For example, many people ask "how do I learn to program video games", and I tell them "learn to program". I understand the same goes for "how do i learn to make digital art" (learn to make art). I would even go so far as saying that this principle extends to design. "how do i learn to design video games" becomes "how do i learn to design", but design is inherently not a fundamental skill. It is built on top of a foundation of skills. Without that foundation, your attempts at design are as doomed as the kid who tries to make an MMO without knowing what TCP/IP is.
His math and programming skills have atrophied significantly. I'm going to work on repairing them. His experiences have given him a uniquely common reason for not having developed a baseline of skill in either art or coding. I'm sorry for being vague, but I am trying to preserve his anonymity. Just trust me on this.