That's a very harsh review of the hacker's diet.
More accurate would be food = energy, exercise = energy expenditure, obesity = prolonged energy surplus stored as fat, and weight loss = prolonged calorie deficit leading to fat reduction.
While I agree that there are wrinkles due to when, how and what you eat, I can't see a problem with that basic maths. You could say a 'bad' calories is one that triggers you to eat more calories, whether that's through habit, or addiction, or stomach stretching, or sugar rushes and crashes leading to hunger. But that still reduces down to more calories.
This book seems to be suggesting that the energy you store as fat comes from somewhere other than the food you eat. That's entering creationism or perpetual motion machine territory for me, and as you would then expect is accompanied by claims that the whole field is crooked.
The rebuttal linked from the article (by one of the "villains" of the book) suggests that the weird data comes down to people lying about what they eat to researchers. Not only do they not record everything they eat, they lie even more about their consumption of fatty foods which (correctly or not) the average person thinks are bad.
This makes it seem like people are gaining weight mysteriously, and that carbs are over-represented. Given the choice between overweight people misrepresenting what they eat and a whole branch of science being corrupt I'll take the former. Particularly if the book writer is happy to cherry pick out the results that he likes and ignore the rest of the field.