If the goal is to have game pass on everything, non exclusive to Microsoft hardware, by definition that is a third party service?
Yes. But Sony and Nintendo won't allow it to be on their consoles unless MS quits from making consoles, limits the gamepass there to published games on their consoles by MS. And obviously, to do so paying them the 30%.
The thing is that MS wants to have their own store and GP on mobile, PS and Nintendo without paying the 30%, instead paying them 0%. Obviously Nintendo and Sony won't allow this unless forced by regulators.
Xbox /Microsoft also publishes game. That is a third party publisher.
Yes
Why bring this up? Because the metric of success in gaming is all messed up: is Microsoft going to then track "games pass is the most downloaded gaming service"(by passively comparing itself to close services ala PSN and Nintendo Online) from "most subscription" from "most hardware sales".
GP never has been always the most popular game subscription in consoles. PS Plus is around 2x bigger. Can't remember the Nintendo game subs numbers but I'd bet it also had more subbers than GP.
By OP's criteria, Nintendo is the only genuine first party left in the industry right now.
Nintendo is a 3rd party on mobile.