So... Sony isn't showing The Last Guardian at E3?
I'd completely forgot about The Last Guardian. It was revealed by Sony and Team Ico (Shadows of the Colossus, ICO) at E3 in 2009, and since then has had little in the way of updates and multiple release date delays.
The last we heard of the game was earlier this year when Sony Worldwide Studios head honcho Shuhei Yoshida said, "We are waiting for the right time to re-introduce The Last Guardian."
E3 website E3insider has a listing for The Last Guardian on their site, with the listing saying: "Check out all the latest screenshots and videos for The Last Guardian, then come back here on Tuesday, June 11 for all the latest details, straight from the E3 2013 convention floor."
Sony has their press conference on June 10, so is Sony planning to re-reveal The Last Guardian? No. No they are not. At least that's what they're saying; and it's exactly what they'd say if they were going to reveal it! Sony said to multiple sites, including Eurogamer and Kotaku that "The page on the ESA site is speculative."