How does it work?!

"The unexamined reason that the weight loss looks so similar at one year
is that the low carb diets call for increased carb levels for
maintenance and look more like the higher carb diets at that point.

Further, the low carb dieters lose more fat mass and preserve more lean
body mass than the higher carb, low fat dieters."

As said, once all is said and done at 1 year weight loss was similar for
all diets because of reduced calories, that is how in all diets it
works. The details might vary to a degree but it is the calories in the
end. Any energy cost for different metabolic pathway engagment is a
detail and not an fundimental explanation.