The game is 1st party.
With Fire Emblem getting its round of previews this week you can expect MUA3 to be pushed next week.
It is only logical given the sales potential of both games that FE gets more focus.
Marvel Ultimate Alliance 3 is a third-party exclusive. It's developed by Team Ninja (Koei Tecmo) and published by Nintendo.
First Party means the publisher owns the developer and the game is made internally for an exclusive platform.
Second Party means the developer works closely with the publisher with exclusives, but isn't prevented from working with other companies/making multiplatform titles.
Third Party means an independent company that creates a game for a platform that may or may not be exclusive.
A third-party exclusive means a game is made by a company not owned by the publisher yet the game is exclusive to a platform. The line between second and third party exclusives is very thin.
Here are examples for this in terms of game exclusivity:
First Party Exclusive:
God of War - Developed by Sony Santa Monica Studios, Published by Sony. Sony owns Santa Monica Studios. God of War is a first-party exclusive.
Super Mario Odyssey - Developed by Nintendo EPD, Published by Nintendo. Nintendo owns Nintendo EPD. Mario Odyssey is a first-party exclusive.
Halo 5 - Developed by 343 Industries. Published by Microsoft. Microsoft owns 343 Industries. Halo 5 is a first-party exclusive.
Second Party Exclusive:
Quantum Break - Developed by Remedy, Published by Microsoft. Microsoft does not own Remedy. Quantum Break is a second-party exclusive.
Spider-Man - Developed by Insomniac, Published by Sony. Sony does not own Insomniac. Spider-Man is a second-party exclusive.
Pokemon Sun and Moon - Developed by GameFreak, Published by Nintendo. Nintendo does not own GameFreak. Pokemon is a second-party exclusive.
Third Party Exclusive:
Bayonetta 2 - Developed by PlatinumGames, Published by Nintendo. Nintendo does not own PlatinumGames, Bayonetta 2 is a third-party exclusive.
Mario+Rabbids: Kingdom Battle - Developed by Ubisoft, Published by Nintendo. Nintendo does not own Ubisoft, Mario+Rabbids is a third-party exclusive.
Journey - Developed by thatgamecompany, Published by Sony. Sony does not own thatgamecompany, Journey is a third-party exclusive.