Those little adapter plugs that come with the sticks are NOT to be used on "just any" stick.
The joystick itself has to be built from the circuits upwards to support USB adapters. If you put this plug on a stick that is pure analog (no USB support at all on the inside) you can damage the stick, damage the computer, and it just plain won't work.
The reason you have to pay $45+ is because the adapter has a circuitboard in it that changes analog signals into USB clock signals. It's not just a plug, there's guts inside it.