The GBI is the Game Boy Interface. Its a homebrew emulator for the Gamecube if I recall correctly though I'm not 100% on the differences between that and the Gamecube's own player.

From what I just saw it is a GBA emulator for any console via a hack
(Wii / PS3 / PS4 / XBOX 360 / XBOX ONE / 3DS ...)

GBI is not an emulator. It really shouldn't be listed as a separate console as it's just a different way of using the Game Boy Player.

This is why it needs to be a platform: http://forums.pokemonspeedruns.com/viewtopic.php?f=117&t=702

I'd still like it if we could separate "consoles" and "methods of play" eventually.  Playstation console variations and things of that nature.