The perception of Artificial Intelligence being some kind of magic is common. However, as with all magic, when you know how it is done it is "just" a combination of techniques skillfully performed. And with AI it is a combination of algorithms, data structures and computational power with an output that make sense for whatever the application is.
The best way I've come up with to explain the current state of AI is, "we can do tricks by hiding multiple immense databases behind the scenes and having supercomputers run complex searches among them, but we probably won't be able to fully model even a mouse brain for at least 10 years... and at that point we'll likely have learned enough new things about brain function to push it another 10 years out."
Not really, unless you count mathematical techniques such as gradient descent optimization or convex optimization as simple. In this case a finite state machine sounds very simple in comparison.
How to make an easily approachable tutorial that combines game-like world and real learning AI (for example Q-learning or maybe evolutionary policy search) remains and open question. Maybe someone will build it.