if there ever is a PS4 GT6, it will probably be run through Gaikai's streaming service. I fully expect that to be a letdown. Essentially, your PS4 is taking your controller inputs, sending them to Gaikai's servers which are running the game you're playing in a sort of emulation environment, and then it's sending that audio/visual data back to your PS4 to display on your TV. To me, that sounds like it will be riddled with input lag.
I don't think that's how it works. It's more like Netflix - it sends the parts of the game you're using, and you play those directly off of the console. Just like with Netflix - it downloads the part of the movie/show you're watching, and will slowly erase unnecessary data that you've already watched, to free up memory space. With games, it's similar, but don't think of it like video. It's not going to forget what the world looks like if you lose connection and turn around. It will stream parts of the maps (textures and objects) that your character will use, and leave far-away parts un-renedered, or with very low-quality textures. As you move across the map, the areas you were once close to may get cleared away, and the farther parts will begin texture mapping and what not. Unless you have REALLY slow connection, I can't imagine you'd be able to see this happening, since it'd be set to download things that you can see, and a bit out of your visual range in preparation for movement.
This is also different from video in terms of size - what it's downloading are wireframes, textures, game physics and mechanics, assets, player data (that bit is probably only a few hundred KB, like a save file), and various other things. I don't know how big these are, but I'm certain that the physics and mechanics and player data will consistently be "installed" on the console during the stream. Anything else will begin to render when the game realizes you are going to use it, like selecting a map, looking at cars, etc. It may even start some pre-renders while looking at your options, like selecting which track, or dealership (if we're talking GT here), and begin to load some of the assets in preparation for a selection. It's more complex than video because games aren't really ever a set path, and you can choose where you go, where video is simply getting the frames you're going to watch next.
I don't really see how game streaming could otherwise work... And that's how it'd make sense to do this "play as you download", as it would download the parts you need to use first. Then streaming could work similarly, just it wouldn't permanently save anything to the console.