Even the Wii itself will run Gamecube games in Wii mode, see "Nintendont".
I was going to say that the GameCube and Wii are very similar to the point where the Wii is backwards compatible but I guess that argument would apply to the Wii U too. Either way, Dolphin doesn’t emulate the Wii U
Yet it does emulate GameCube and Wii, completely separate consoles.