For arguements sake (no disrespect intended)
In the video game industry, a first-party developer is a developer that is part of a company that manufactures a video game console. First-party developers may either use the name of the company itself (like Nintendo), have a specific division name like Sony's Polyphony Digital, or have formerly been an independent studio before being acquired by the console manufacturer, such as Rare or Naughty Dog.[1]

As sin and Punishment 2 was developed by Treasure, it is not a first party game. Nintendo owns no part of Treasure.
Star Successor is an exclusive. Nothing more.
Monster Hunter Tri was Published by Nintendo in Europe and Australia, does that make it a first party game? Nope.