Cool demo but I still wonder if fundamentally this is just a brute-force approach. Wouldn't it be better to do some traditional preprocessing (e.g. recognizing rectangles, circles, etc.) and feeding higher-level descriptors into the classifier?

If the net learns based on pixels you still have to somehow solve rotation and scale invariance. Or is there something new in deep-learning vs. old-school neural nets that fixes the issues that bedeviled neural nets the first time they were popular?