problems with the above:
TMNT was by Palladium, and it was particularly hard struck by Simbieda's ill-mannered approach to organization and copy/paste form of publication. Not an easy one to learn by oneself, especially if one is young.
Kobolds and Ninja Burger rely *exteremely* heavily on the referee creating the stories and adventures by him/herself. If you are running the game for your kid, and you think you can pull it off, great. These are particularly silly games, and therefore well suited to kids who are into monsters and ninjas and the like. They are simple and easy to learn, and Ninja Burger even requires you do hand motions when your character uses ninja magic -- a fun and involvign twist for high energy kids. However, if you are going to have a hard time organizing an adventure (and it's not as simple as coming up with a plot, there's balance and participation and multiple solutions to work out) -- these might not be as good.
The D&D Basic Game is a "board game" style approach, but uses D&D rules. If you can get it, it'd be a good way to teach, because they can visualize it more easily. It is, however, subject to D&D rules, as I said. Which, depending on your view, can be good or bad. I wasn't more than 8 or so when I learned D&D, and I believe AD&D back then was a little bit more of a morass than 3.5 is today.
There's a game whose name escapes me that would be perfect however, and if I can get ahold of Jeffe, he will remind me. In it you actually play children, the sons of the ruler, and you go around the kingdom taking care of the problems. I keep meaning to try it with my girls, but we all know how things like that go.