According to Xbox One representatives this afternoon, it's not just the PlayStation 4 that'll be offering the ability to play downloadable games before they're fully downloaded once the consoles launch later this year. Speaking up after the fact that Sony's console would offer such a service - and perhaps seeing the high-fives and thumbs up given in response - Microsoft has issued a statement on their machine's ability to work with downloading games well before they're fully downloaded.
It's not that the Xbox One couldn't always do this, it's just that Microsoft more than likely wants to make clear that they're not letting their customers behind. This ability also works with the installation of games from disks. According to Microsoft as well, you'll find your ability to play the game appearing well before a physical disk is done installing your full fare of data.
"Consumers will be able to sign on to any Xbox One console and have access to all their digital games. Once the required data -– a fraction of the entire game -– is on their hard drive, they can jump into the action while the rest of the game finishes downloading in the background." - Microsoft Representative
Both the Microsoft-made Xbox One and the Sony-made PlayStation 4 will be launching near the end of this year, well within the bounds of the 2013 holiday season. At the moment we've not yet seen final builds from either company, so demonstrations of the abilities described above will not be available for viewing for some time. At the moment we're left with sly not-quite-real-and-full access, as it were.
The ability to play games well before they're fully downloaded or installed exists on the Xbox 360 right this minute, and most web-based gaming hubs allow this functionality from gaming PCs here in the summer of 2013 as well. It's not that we've never seen this sort of quick access before, it's that the public wants to continue to see it happen well through the future.