Not really. As I understand, the different layers are:
1. In-game, he can write non-arbitrary but sufficiently powerful machine code to be executed directly. He uses this to write layer two.
2. He can write arbitrary machine code using A, B, start, select. He uses this to write layer three.
3. He can write arbitrary machine code using all the buttons (including d-pad combinations that I assume are physically impossible). He uses this to write the balloons.
All the code that actually gets run is precompiled machine code being executed by the processor. (There's nothing to stop him writing a shell, he just didn't.) He's not exploiting a system which happens to be turing-complete, he's gaining access to a system which was designed to be turing-complete but locked down.
