That is absolutely the way to go, is just tell the kid "did you know you can make your own games on the computer?" The kid will likely fall mostly into one of three categories:
1. Disinterested.
2. Is blown away by the thought of making his/her own games and obsesses nonstop on programming of various kinds for probably their entire life. This might sound like an exaggeration, but the video game industry actually has a reputation for having these die-hard developers who work insane hours and love every minute of it (unless they're with a big dumb corporation).
3. Somewhat interested, looks into it, finds that it's really difficult and quits relatively early. Maybe the kid will even put a few demos together or something, but game programming is hard. There are few branches of software more difficult to develop. Most kids will fall into this category, I'd bet. But the good news is, this person may have a chance to still be really interested in programming and go on to have a great career writing other types of software.
It sounds like #3 would be just fine with this person, and I think it's a really common trait. I'm a programmer myself and many of the other devs I've talked to got into it by putting together a little game in QBASIC or whatnot.