This is not the first time microsoft has published third party similar to Sony's games

[pokoko]

Rafie said:

When a 3rd party developer develops a game exclusively for a platform, it's a first party game?

It's like this:

If Microsoft owns the rights to an IP then it is ALWAYS a first-party game, even if the game is made by a third-party developer.  That situation is often called "second party," though, as I said, that's really just short-hand.

If Microsoft does NOT own the rights to an IP then the game is third-party, even if it's an exclusive.  That just means the two companies signed an agreement to keep it exclusive.  We call it a "third-party exclusive" as short-hand.

Same for Sony or Nintendo or whomever.