Is the Super smash bros for Wii u controller itself (not the adapter as I know it's not compatible) adapter compatible with an original Wii or GameCube? I don't want to purchase used ones from Ebay because I heard about lots of Ebay scams.
As @Powerlord pointed out, the GameCube Super Smash Bros. Edition Controller is compatible with the original GameCube and Wii. This is confirmed on Nintendo's website (in the same link provided, very last question)
Can the GameCube Super Smash Bros. Edition Controller be used with a GameCube or a compatible Wii model?
Yes, it can be used with these systems.
Sidebar: Always make sure to check the box before confirming your purchase! 3rd-party companies like Hori and PDP make their own "Fight pads" as well, but they're Classic Wii controllers without the analog triggers. (They have squishy triggers, but there's no analog signal, and that means tossing your shield or grab is delayed significantly.