Apps/games on the Apple TV are limited to 200MB plus can download up to 2GB while in use. The second you exit the game/app, that space is free to be overwritten by anything that needs the space (like another game).
Because of the huge bandwidth requirements of doing this, it's unlikely most games will have a lot of downloadable bits as even 500MB becomes huge when you consider thousands of users will be downloading it almost every time they play your game.
Unless you like storing tons of photos on the device or lots of games you're unlikely to play often, the 64GB doesn't really offer much advantage.
The flip side of that of course is that the system isn't going to overwrite data willy nilly. If there's empty space, it will use that before deleting data that's in use. So the more free space you have, the less often you'll be downloading things.
The 2.2GB on device storage isn't as bad as its all made out to be either really. On iOS you get a total of 4GB of space for your app. But that's up to now included assets for every device.
With app thinning some apps, of course it won't be all, have managed to get their size down by 50% or more for each individual device. So that would mean, theoretically, many apps that exist would fit into the 2.2GB space requirements of the Apple TV.
Of course that's not always going to be the case but even when an app has to use on-demand resources, if it's intelligently designed, the end user should never notice it at all. The caching will be performed in the background, ahead of it being needed, so by the time you get to the point of using it, it's already there.
It's not a perfect system, I'm not saying that by any means. It's a poor relation to having everything stored on the device. But neither is it a terrible system either. Aside from a user suffering an internet outage at a coincidentally crucial stage of a game. You should never even notice it's happening.
