This morning Activision sent out a press release confirming that Destiny will not see a 2013 release and officially confirmed that the game will be released on the Xbox 360 and PlayStation 3 as well as "other future gaming consoles", which we can safely assume are the PlayStation 4 and next Xbox. With Sony's big PlayStation 4 reveal meeting only a couple of days away, it is not too farfetched that Destiny might be demoed at the event to showcase some of the PlayStation 4 capabilities.
Furthermore, about a year and a half ago it was reported that Naughty Dog had been talking with Bungie and Infinity Ward. Naughty Dog being one of Sony's biggest and most popular studios, are most knowledgeable when it comes to developing games for Sony's tech. What exaclty the nature of the "help" they gave Bungie and Infinity Ward was never revealed, but it could very well have been tips for working with PS4 code.
With these things in mind, the few gameplay snippets shown in Bungie's video are most likely running on next-gen console tech, and the public just might have caught the first look of the PlayStation 4 in action.