I believe those are serial devices 'like' PS/2 mice, so you would need a software driver as well.
Yes they are serial devices, but, you do not necessarily need drivers, well, not for the Amiga that is. You can as well put a microcontroller (like an AVR), and upload a driver to that. I remember I saw it once, a demo of the nes controller attached to an Amiga. Then again, if there isn't a driver for it, my guess is that it won't be much of a fuss to make one yourself, if you can write c code. As the nes controller has 8 buttons (4 direction buttons and 4 action buttons (start, select, A, B) my guess is they put the controller status in one byte, one bit for each button. The only thing to find out is what kind of physical and connection protocols they've used (my guess is RS232, as it is the most common and therefore most likely the cheapest for them to implement).
Though you WILL need cut the controller cable because the nes plug is proprietary (IIRC). Though you can as well make a pass-through, as the cable is quite long.
-edit-
some more informationHm, so I was wrong about the RS232 part. Perhaps back then it was too expensive, and/or too slow for this purpose.