The whole industry always considered first party the games published by the platform holder, independently if they own the IP or the lead dev studio or not.
In this case, in addition to first party the game is also 2nd party. 2nd party are the first party games with a lead dev studio not owned by the publisher.
A few days ago I shared a public legal document from Shift Up to their investors and Korean authorities where Shift Up says that Stellar Blade is a 2nd party game (which means it's a first party game).
1st party game means published by the platform holder.
Meaning, the PlayStation games published by Sony are 1st party (like Death Stranding), and the ones published by everybody else there are 3rd party.
It also means that in Steam the games published by Valve are first party and the ones published there by everybody else (like Sony or 505) are 3rd party.
CoD now is a Xbox 1st party game and a 3rd party PS game.
Death Stranding is a PS 1st party game and a 3rd party PC game.