This is why the term "second party" exists.
A game that is developed and published by the first party is obviously first party. A game that is developed and published by a third party is obviously third party. The term second party exists to describe a relationship where a third party develops and a first party publishes.
Team Ninja is contractually obligated to make THIS GAME only for Wii, so as far as this game is concerned, they are a second party developer. Second party is an informal catch-all term for when a first party and a third party collaborate.
"[Our former customers] are unable to find software which they WANT to play."
"The way to solve this problem lies in how to communicate what kind of games [they CAN play]."
Satoru Iwata, Nintendo President. Only slightly paraphrased.
