The study is paywalled but from the article:
The high-fat group followed something of a modified Atkins diet. They were told to eat mostly protein and fat, and to choose foods with primarily unsaturated fats, like fish, olive oil and nuts. But they were allowed to eat foods higher in saturated fat as well, including cheese and red meat.
[...]
The low-fat group included more grains, cereals and starches in their diet. They reduced their total fat intake to less than 30 percent of their daily calories, which is in line with the federal government’s dietary guidelines. The other group increased their total fat intake to more than 40 percent of daily calories.
Of the three macro-nutrients protein is known to be the most satiating per calorie.
And things that are high in protein (meat, eggs, nuts) tend to be the same things that are high in fat. While things high in carbs (grains, starch) tend to be low in protein.
So a big effect of a low-fat diet will be fewer calories from protein, and a low-carb diet will mean more calories from protein. I'm almost certain that the low-carb group ate a lot more protein than the low-fat group, and I'll bet that was responsible for the additional weight loss.
This is important because it means these results are completely consistent with the hypothesis that fat is the most fattening macronutrient, followed by carbs, and then protein being the most thinning. The reason why low-carb was the most thinning is that the weight loss caused by the additional protein overcame the weight gain caused by the additional fat.
Can anyone with access to the study confirm if there were big differences in the protein intake?