It is 100% a gamecube game that got held back (for the millionth time) so that it could be released on the wii too. Saying it is a Wii game is like saying any port/re-release onto a new system makes it that game. Like OoT being a 3DS game because they re-released it.
I consider it a gc game mainly because that's what I first played it on and because I think the wii controls weren't that good for it. If it was really designed for the wii I believe they would have worked on the motion controls more and could have made something close to what skyward sword had
Sadly, I only have the wii version of TP. But I willingly admit. I wish I had the GC version. I say, it was meant for gamecube but it came as launch with the wii for sales most likely. Although, it's the same game, just mirrored, so I guess it doesn't matter which of the two consoles you play it on really.
the Wii version of Twilight Princess came out first in Europe, America and Australia, and Both versions came out on the same day in Japan. That said, Twilight princess was originally intended for the Gamecube but was delayed so Nintendo could port it on the Wii and add extra bits of content. So really Twilight Princess is a Gamecube game.