Presumably, game developers would serve up the game to the browser via localStorage. This would make the experience very similar to Steam today, where you download the game, then play it.
You could even design the game to be downloaded in chunks. Download the first level, and while playing, download the second in the background. This reduces downloads and load times.
LocalStorage is 5-10 MB per domain (currently there is a bug in most browsers that allows you to bypass this by using subdomains, but I wouldn't count on that being the case for much longer).