I was interested in these things for a while in so far as their bendability potential. After some time searching I found out what the insides of an Atari stick look like. There is a crystal and some blobs. A few obvious techniques can be tried, like switching it out the crystal or short circuiting its legs. Curious to explore I decided to cough up $9.87 for one at Walmart. To my surprise there was quite a selection ranging from Atari to Sega with everything in between. All I am assuming to be console-on-chip combinations, Like the NOAC.

The one I purchased comes from some No-name company in China (well KidConnection actually) and is simply called Joystick 30. It does contain 30 Games with sounds and video resembling NES! One big difference from the Atari version pictured above is that all the roms are stored on a 32Mb Flash Rom chip called M5M29GBT320VP and I was able to get the Data sheet on it pretty easy. From the datasheet I concluded that this flash rom chip is fairly easy to burn data to. Meaning that if someone was so included as to reprogram the Joystick 30, they can very well do so with some basic hardware. Unfortunately that someone is not me, at least not yet. But the possibilities are limitless. Imagine a MIDINES all enclosed in this joystick with a Nanoloop like sequencer. That would be awesome! And for $9.89 the price is definitely right.
I have not started bending this one, but from what I can tell it will be fun.