That's one part of it, yes. A browser API providing a few GBs of persistent storage with proper isolation and user management, obviously with some kind of compression/decompression going on to save both download times and loading times.

As an example, consider Infinity Blade, the poster child of mobile gaming: released in 2010, 595 MB download, 948 MB installed. Even the first version of WebGL is capable of providing this kind of experience, we just cannot get it to the user via browser.