Disney didn't make your TV
Analogy != perfect. I've seen Disney licensed TVs in Wal-Mart stores. These are 13" or thereabouts and apparently intended for a child's room. I've also seen Disney licensed DVD players.
Disney also puts its name on clothes and everything else imaginable, but it's still known for making kids' cartoons.
Contrast this with the Wii, where it matters not who made the game, it is known to its users as a "Wii Game", and thus has a direct association with Nintendo's brand and image.
Do Windows games have a direct association with Microsoft's brand?
No they don't, because Windows has a multitude of uses besides gaming, but Microsoft sure wishes that people would associate games directly with them. They wish it so much that they actually created a dedicated piece of hardware that only played video games. Now people do associate video games with the Microsoft Xbox.
You play it on a Wii, it says "Nintendo" on the packaging
In that case, Nintendo made its own bed by using lockout chips to shut out unlicensed software.
Yes, Nintendo did make its own bed out of solid gold bullion and wove a comforter out of million dollar bills.