The versions listed are just what platforms the games released on, not the console played. You can use whatever console you want
I'm fairly certain that Wii is allowed, I used to run Wii before mine broke and I think there are some other people that run on a Wii. If your run is Wii I think you should just submit it as GameCube.
I think the actual console you played the game on should be listed as an option while submitting, not just the platform the disc is for. For instance, if you play a PS1 game not on an actual PS1, you should be able to submit as PS2, PS3, PSTV, or whichever piece of hardware the game was played on. So I think Wii, PS3, and Xbox360 (?) should be added as console options when submitting.
As far as I'm aware, there's no difference in playing on a Wii or a Gamecube, it's really just what's convenient for you.
