I've been teaching my kids how to code on and off since they were six. At a young age, it's better to think of it as creating animations using Scratch or similar. The older they get and they more they're already playing games, they'll be better at making games.
A good way to start is with code.org.
Coding is much more fun if you can share your work with others. If the kid can bring an iPad to a friend's house, great, use Hopscotch. If you want to email a link to your game to Grandma, you should probably use Scratch but until Scratch 3 comes out, Grandma will have to have Flash installed.
If you have Android devices lying around, try MIT App Inventor.
On each of these pages, you'll see more of my thoughts on the various options: