Errr.... consuming 6000 calories and burning off only 1300 would cause you to gain more than a pound. That might be a daily intake for someone weighing 600 pounds, but it's hardly the situation for your run-of-the-mill fat person.
Putting it in practical, personal terms -- I was laid up for six weeks for medical reasons this winter, and my bad habits continued for the next six weeks as well. Over that period I gained about 18 pounds, one of the worst periods of weight gain in my life. Simple math (and ignoring the data presented in the article!) tells you I must have been eating about 5250 excess calories a week. Roughly speaking I was probably eating 23,000 calories a week when I should have been having 18,000.
Now suppose I had gained that weight on a low-fat diet. The study cited in the article suggests that if I had been on a low-carb diet instead, I wouldn't have gained any weight at all! That's a pretty significant result. (Of course, in practice I was on a "whatever" diet.)
For those of us living on the edge, trying to shave off 500 calories a day, the knowledge that not all calories are created equal is a Big Deal.