Is the video real? Sure. Did he really need every foot of runway? Maybe. One explanation is that the pilot accelerated longer on the runway to build up more "smash" and pulled 'er off at the end. Is that possible? Sure.
When pilots fly the same airplane, big or small, day in and day out, the only way they genuinely get in a situation like this is to screw up big time, either with the gross weight of the bird or when computing their takeoff data (including a reduced power selection). Not only does experience tell you what's "doable" before crunching the numbers, but crews experienced with these big birds will also employ techniques such as an acceration time check or measured acceleration distance to ensure the airplane is performing properly long before getting to an abort point - not to mention the departure end. No, his climb-out path is not stellar, but he's not dragging the trees for miles either.
I'm a skeptic at heart.

If it were really a goof (including computing no data at all), I'd've expected to see a much more aggressive rotation, given that the end was rapidly approaching. Also, look at it this way - if the airplane were overloaded, what are the odds that the overload was exactly such that it would lift off exactly at the end? Odds are that it'd lift off earlier ... or go long, but not need the precise length available. To me, it's more plausible that he chose his rotation spot, however gutsy it may have been.
One man's opinion.
Ken
767/757/737/727, DC-9, C-130