To apply pressure on the US government regarding the revocation of his passport making it impossible for him to reach Ecuador or where ever, of course. He's stuck in Moscow due to his passport being revoked and Putin's basically told him that he's not welcome there. He's in a tight spot.

You'll notice he never once mentioned the documents or their contents in this message. He's not "making the story about himself" - he's using the media as a tool to apply pressure to the forces aligned against him in the hopes of securing his safety.