I need to be sure.
So I can essentially just publish a game from Gamemaker 2 Desktop Edition with nothing like giving some money to the company like with Unity or something?


You don't need to pay any fees to YoYo Games.

However, if you plan on exporting to Mac, I'm pretty sure you need to pay Apple for a developer's license. I forget how it works. But if I remember correctly, GameMaker doesn't even let you export to *.app if you don't have the Apple developer's license. (The developer's license is subscription-based. I think one or two hundred dollars for a year, and then you need to pay again each year when it expires. Kind of a ripoff, but I did it last year because I needed to export an early prototype of my game for a school assignment :( Now my Apple license is expired so I'll need to pay again once I get around to finishing the game.) Additionally, if you plan to export to Mac *.app then you'll need a Mac.

As for other platforms, I don't know. (Never tried exporting to Windows or to anything else.)