Is Metroid: The Other M Considered First-Party or Third-Party?

[Smashchu2]

Here's the explanation on it, if no one has given it already

First party games are games developed and published by the same company (so, a mario game made by Nintendo EDA and publsihed by them is first party)
Second party is where Nintendo is the publisher, but not the developer (so I guess it is a second party game)
Third party is where Nintendo is neither the developer, nor the publisher. However, it is still on their system (so Red Steel).

Now, there are second party developers (like HAL labs). This is where Nintendo has a contract with them, but does not own 51% of the development studio. Third party is a developer who is not tied to Nintendo.

So I'm not sure if a second party game explanation was correct. Other M is either first party or second depending on the definition of second party games.