Discord definitely checks your process list, that's well-known and obvious (by default it shows everyone which game you're currently playing, if any).
Given that that information does go to the server, there's no way to know what it's used for.
Given that that information does go to the server, there's no way to know what it's used for.
That "given" there is doing a lot of work. I've never seen any reference stating that it's sending the entire process list anywhere.
The current third party protocol implementations all expose setting the game/activity you're playing directly, sure making it look like everything is done client-side.