So they concluded that the D800 didn't blow the 5DIII clear out of the water. They obviously have a Canon bias, and their video is bogus
Seriously, though, to summarize their findings:
1) The D800 has a resolution/detail advantage, but not enough to really matter in most situations.
2) The D800 has a slight advantage in DR, but it's hardly noticeable.
3) The 5DIII has a snappier AF system.
4) The 5DIII has slightly cleaner high ISO images at the expense of smudging detail.
5) The 5DIII has "punchier" raw files
6) Both are amazing cameras and you can't go wrong either way.
To me, #5 is why I shoot Canon. The D800 is a brilliant machine, but I just don't like the look of it's files as much as the 5DIII. "Punchy" isn't exactly a scientific term, but the 5D line has always had a certain balance of color and contrast that give their files such a pleasing look. That's more important to me than some lab test results, but to each their own