I personally think that you're on the right track by choosing Unity.
With VERY little programming background I was able to make fully functioning games within my first few days. You can explain the basics in less that 5 hours and let them have at it creating, leaning, and most importantly enjoying game design.
The engine itself is very powerful and once they start getting the hang of UnityScript if you wanted to introduce a more rigid programming language you could do so with C# which is also supported by Unity.
Unity has been released for FREE so you should have no problem supplying it to your student. The Pro version has its pluses especially for stereoscopic stuff, but I don't think you'll be introducing that very early on. The free version will most certainly be enough for beginners and even intermediate students.
Did I mention the huge amount of resources available online for it:
The community is also incredibly helpful! I know because I've received plenty of help and guidance.
It's ideal for rapid prototyping which is what I tend to use it for, however it can serve as an excellent resource for learning game design and even programming without getting bogged down with the low level stuff.