No, the jig is not a mod at all. Neither softmod nor hardmod. This is because nothing is modified bythe jig
It is a mod. It modifies default hardware behavior by including a button that is not present in the system. It's only not a full on hardmod because it's not permanent, just like flashing the xbox360 dvd drives in the old days - no permanent changes to hardware, only a software update to the drive Firmware. But you DID tamper with the hardware, opening the xbox and connecting it to a PC. By doing so, even in the smallest way, you are already out of the realm of pure softmodding.
In summary, it's not a pure softmod, as it relies on hardware tampering. It's not a hardmod, since said tampering isn't permanent. It's something in between.