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You need all the art and sound for the first few minutes. Probably a lot more than 300MB.

PS4 has gone this way already. When downloading a game you might get two progress bars. You can start the game when the first one is done, and it will download the rest of the game while you're playing. Microsoft has had this tech for a long time, I know they use it for MS Office programs at least.

Browsers are pretty terrible at downloading more than a few hundred MB. They can't compare to native download managers like Steam or Blizzard's, or even wget.