Sony seems to following in the footsteps of Bethesda and its radio silence for Fallout 4. In an interview with GameSpot, PlayStation boss Shuhei Yoshida provided the main reason for why Sony is not showing anything about The Last Guardian, possibly until it's actually released:
Development is going well, but because it's about the story, we don't want to show too much.
We wanted to show that it exists, it works, it runs. It's not like we won't show anything before launch, but I think we will try to limit what we show about the game.
While this isn't exactly the best plan of attack for the gaming press (us included), this is ultimately better for the game and leaves that certain air of mystery that carries artful games like these. As the spiritual successor to ICO and Shadow for the Colossus, The Last Guardian is relying on an artful, textless story to sell the game just much as the precarious platforming.
No specific launch date hasn't been specified apart from 2016... not like we aren't used to waiting for the game to come out anyway.