Is banjo threeie on GameCube a proper game?

There is no game called "Banjo Threeie" on the GameCube.

It's possible you're thinking of "Banjo-Kazooie: Grunty's Revenge" which was released on the GameCube in 2005. It's a proper game, although it's not considered one of the main entries in the Banjo-Kazooie series.

Let me know if you're thinking of a different game and I'll try to help!