No, it doesn't. I don't think that you understand how an overlay works. You run a command or modify a configuration file to add the overlay. Then you can install any packages in that overlay. Those packages would be the games.
The package manager on Windows (Steam) isn't needed on Linux because there's already a native package manager on the majority of distros. In fact, you can already buy games through the Ubuntu package manager. I believe they're in a separate, "partners" repository. Steam should just be another repository like that.