Writing for Polygon, Dave Tach has an in-depth overview of how games will be installed and work on the new Apple TV:

Before app slicing, Apple treated apps as all-or-nothing bundles. That meant that you couldn’t start playing Barbie: War until the multi-gigabyte file that included levels one to 10 (and all of the resources created for other devices, resources you didn’t need and would never use) finished downloading. But with a combination of App Thinning, slicing and on-demand resources, users can get the essential components of a game — things like the executable code, the splash screen that loads when you launch the app, the title screen artwork — in the initial download and reserve downloading for, say, levels eight to 10 until players approach them by completing the prerequisite levels. Levels four to 10 live in the cloud, tagged, and Barbie: War’s developers can say when the game should start downloading the assets tagged for specific levels.

This is possible because Apple provides developers with cloud-based storage accessible at any time — or on demand.

Tach goes on to explain how tvOS will manage app installations, and he also interviewed some game developers on their thoughts on the new Apple TV. I’m really curious to see how all this will work in practice.