Things they cover: the bomb calorimeter, a couple of adjustment lists for when humans digest things noticeably differently from what the bomb calorimeter says is in the food. The observed fact that people with different gut bacteria seem to get really different amounts/kinds of things out of what otherwise seems to be the same food. Attempts to measure basal metabolic rate.
Their conclusions are conservative. If nutritionists think we should reduce calories in by a couple hundred calories a day to lose weight, and all of the above plus the usual issues with accurate portion control mean that we probably can't reliably _get_ control over total calories in accurate to the hundreds place, then no wonder dieting doesn't work.
Also, their recommendations are conservative: focus on diet composition and satiety, rather than calories.
They do have some speculation: personalized recommendations. But the overall thrust of the piece is unwarranted in its optimism:
"There should be a better metric ... And it’s likely there will be. Science has already shown that the calorie is broken. Now it has to find a replacement."
Let's pretend for a moment that we actually could measure calories in accurately. (Bwah ha ha ha ha) PRETEND HARDER YOU ARE DOING IT WRONG How does this help? The equation is calories in vs. calories out. If you want to gain, you must consume more than you use. If you want to lose, you must consume less than you use. HOWEVER the primary user of calories is basal metabolism(I'm assuming that we are not allowing people who exercise to the tune of 20 plus miles a day or their caloric equivalent to participate in this analysis. Go. We're not interested in you.), and we already know that the more you eat, the more that sucker consumes -- and the less you eat, the less it consumes. (Homeostasis For the, well, something.) And we are actually really bad at estimating basal metabolic rate in a given person who is attempting to modify their gross health metrics.
Screw this calorie thing. Let's figure out a cheap, portable, accurate way to measure BMR. Not BMI. BMR. And then in addition to whatever other crap you measure (waist, thigh, weight, etc.), we should also be measuring BMR. And if BMR takes a nosedive, it gets priority one for improvement, because everything else is gonna get worse until we do.
ETA: Apparently I should not say BMR. I should say RMR.
I am not endorsing anything else these people are saying.