Nintendont works in Wii mode (not gamecube mode or wiiu mode).
it rewrites the gamecube function call (in the game) to the wii mode function doing the same thing. for example, when nintendont see the game requesting a function to read a texture, it takes the game's request and send it to the Wii texture reading function instead.
Nintendont know the location of the function in Wii and vWii mode. the wii is working globally like the gamecube and can share the same functions.
I don't know if the WiiU could do the same, maybe the functions uses different arguments number, or return different values, etc.
it would require a full function patch rewrite to do the same with a different CPU architecture.
at least, all 3 console use PPC CPU, so it only need a "function patch" and not an emulation of the CPU.
Like said above, the best you can do to play on the gamepad currently is to display the vWii picture on the gamepad, unless there's a way to enable the controller's button in vWii mode (the same way WiiU VC Wii titles works, like xenogears launched from wiiU with gamepad buttons input enabled). It will still be in "wii mode" but the button could be active.
If the "Wii VC" is the exact same game than the Wii game, and is not managing the gamepad's input, then it's the IOS or the WiiU itself which is allowing access to the gamepad input while in Wii mode. we could always enable that option when launching Wii mode.
if the gamepad input is part of the Wii VC game, then it will be harder to enable it for all Wii mode.