I had to inquire with the fine folks at Poly.Play about how this is supposed to work. But I got a very informative response and links to some excellent technical documentation. Here are the three articles necessary for having a full understanding how this works:
Learning about how the Super Nintendo Controller works was a cool experience for me. A nice and simple example of how digital electronics works. It's a very clean and easy to understand example of a serial data protocol, that makes use of a data line, a clock signal line, a reset line and a shift register. The ability to understand this era of computer technology is one of the things that makes using a Commodore so appealing as a hobby.
The Trap Them Controller is effectively a Super Nintendo Controller with the cable swapped for one that ends with a standard DB9 joystick connector. However, the documentation on this one is geared for how to get the Commodore to interface with the serial protocol of the Super Nintendo Controller. The article includes how the controller's lines are connected to the C64's lines. And also includes an example assembly language routine for how to read in the status of the buttons. Typically you'd do this 60 times a second, alongside the keyboard scanning routines.
Once you understand how the above two parts of the puzzle work, the SUPER PAD 64 is an adapter that plugs into both joystick ports on a C64 or 128. And it provides 8 controller ports for regular Super Nintendo Controllers. Of the C64's 10 digital lines (5 per port, up/down/left/right/fire) two of those are used for clock and reset which are sent to all 8 controllers in parallel. And the remaining 8 lines are for the 8 individual data lines from the 8 controllers.
The routine to scan all 8 controllers is a bit more complicated, but the routine used for the Trap Them Controller should be perfectly compatible with a controller plugged into one of these ports. So the SUPER PAD 64 is compatible with anything that can use the stand alone Trap Them Controller. That's good, because the biggest problem with this adapter, in my mind, is lack of software support.
But, like any newish adapter for alternative controllers, like the 4-player adapter, the more that developers just take the plunge and write software to support it, the more valuable it becomes for people to take the plunge and purchase one and that can become a virtuous cycle.