What you’re looking at above is the official UAPROF (User Agent Profile) for the Samsung Galaxy Note III. A UAPROF is used by content providers on the web to create content suitable to that device. So in the UAPROF for the Galaxy Note III we find that it will indeed have a 1920 x 1080p display.
As for the size of the display, it’s rumoured to be around 5.7-inches. Other rumoured specs include Android 4.2.2, a 13MP camera, 3GB of RAM, thickness below that of the Galaxy S4 (7.4mm), a sizeable battery, and a quad or octa core CPU depending on the region.
Samsung are expected to unveil the Galaxy Note III at IFA 2013 in Berlin which runs from September 6th to the 11th. So it’s a little while off yet.