Apple TV games are still capped at 20 GB but you can now download up to 4 GB right away!
From Apple Developer News:
The size limit of a tvOS app bundle has increased from 200 MB to 4 GB, so you can include more media in your submission and provide a complete, rich user experience upon installation. Also, tvOS apps can use On-Demand Resources to host up to 20 GB of additional content on the App Store.
There were two things that hurt Apple TV when it came to big game support at launch: The last-minute requirement for Siri Remote support for almost every game, and the 200 MB cap on initial package loads for on-demand resources (ODR). The combination led to many studios who might have taken a risk on the platform because it shared the same logo as iPhone to sit back and wait, and ultimately to take a pass.
I never really understood the Siri Remote flip flop at launch. Yes, it meant no one had to feel "bullied" into buying a second, separate controller just to play a game they liked. But it also forced developers to figure out how to graft on a sub-optimal control scheme when all they wanted to do was launch their games.
The download limit was easier to understand — Apple wanted people to be able to keep a great variety of apps available and never have to see or handle a "storage full" error. But it was another pain point for developers,who had to go to the extra effort of slicing up and staging their apps for Apple TV in a way they didn't have to for other platforms. It also wasn't a clear win for customers who saw less storage errors but had to sit through more download screens.
Apple dropped the Siri Remote requirement with last year's tvOS update. Now they've expanded the initial package download from 200 MB to 4 GB. The overall size is the same, with ODR managing up to 20 GB total, but the change in initial download represents a 20x increase, and that's huge.
Personally, I hope big studios that did choose to sit Apple TV out at launch take another look now. Just like MineCraft has. Also talking to you, Nintendo...