Best answer: There is a wide selection of newer games that can play certain missions or parts of the game as you download. However, none of them will let you play the whole game until the download is complete.
Selective downloading is great
The PlayStation 4 ability to play games as they download is great. It lets you get a taste of the game as you wait for the full download by selectively choosing what parts of the game to download first. This means you can play the intro missions, character selections, or sometimes, whole game modes, while you wait for the rest of the game to finish.
Game developers actually build selective downloading into the game itself. They submit to PlayStation a list of files to download first, so they are queued into the download list first by the Sony servers. They can even go so far as to give the user — that's you — the option of what parts of the game they want to download, though I rarely see that happen.
You could, in theory, choose to download just the single player, or the multiplayer parts first, letting you play the part of the game you like the most as quickly as possible. This makes a lot of sense to me for single-player games that have a multiplayer component tacked on. If you don't really care about the multiplayer aspect, download the solo game first.
Anthem has this feature
Anthem is the latest release from EA and one they hope to make into a huge franchise, and it allows you to play some of the features before the game is fully downloaded. You will still need to download 13GB of data to play any of the game, but 13GB takes much less time than the full 39GB game file.
When that first 13GB is downloaded, you can launch the game, play through the first mission that sets up the world of Anthem and even go through the character creation mode, all before the full game is ready to play. Now, this isn't a huge amount of content — maybe an hour or two at most — but it does get you that fix of Anthem you need while you wait for the full game to make it onto your hard drive.
It doesn't work for all games
Not all games have this feature. Although most of the latest releases do, some smaller games and none of the PlayStation VR games I have seen support it. For smaller games, that makes sense, since after all, they are usually a smaller download file so it shouldn't take them too long to download anyway.
The PlayStation 4 Pro is a powerhouse.
The PlayStation 4 Pro is the pinnacle of PlayStation's current generation gaming console. With its ability to run 4K games at incredibly smooth framerates, the PS4 Pro is the go-to choice if you are looking to purchase a console.
Explore a whole new world
Anthem is the newest open-world shooter from EA that promises to take the world by storm. With a huge overarching storyline and exciting battles, as well as flying robo-suits, Anthem is a game to expect great things from in the coming months.
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