It means the Wii Virtual Console version specifically. Using a Wii Homebrew emulator would be classified as an emulator run (although the only emulators allowed are Project64 1.6 & 1.7).

If you're on a homebrewed Wii you can get a .wad file for OoT and then that counts as VC

but you need a classic controller to play on the wad version, don't you?

No, a GameCube controller will work as well, assuming you’re playing on a Wii and it has GameCube ports. Y, Z, and X map to C Left, Down, and Right respectively as well. There are also N64 -> GameCube port adapters you can get it you want to use an N64 controller.