Wii games don't run under another application. They run using the IOS they were written to support or a cIOS that you have installed and specify in the Wii loader. GC games don't actually run under Nintendont either once they're loaded. Nintendont patches its code that redirects the disc interface, etc., into IOS 58 then starts the game.
If you have Wii games selected in the categories on USB Loader GX and they're not showing up then they're either not in a valid folder or the drive isn't partitioned/formatted correctly.
GC games: /games/game title [titleid]/game.iso
Gamecube: "/games/Game Title [TitleID]/game.iso" (or "disc2.iso" for second disc of two-volume games)
Wii: "/wbfs/Game Title [TitleID]/TitleID.wbfs" ("TitleID.wbf1" for the overflow file if the game is >4GB and you have them split)
All loaders are compatible with that naming scheme.
Wii gameS: /wbfs/game title [titleid]/titleid.wbfs