It's sure a way to sell a book, but does it make any sense? In my opinion the author's theory is just another distraction from the simple truth that for most people running will result in healthy weight loss, to a point, and then maintenance of a healthy weight.
The claim is that our metabolism would slow down for the rest of the day after exercise - below the metabolic rate that would apply if we did not exercise.
This means that If I were to run 10km and burn 600 calories and on these days I ate more than days I did not run then I would put on weight. For me, the claim doesn’t pass any plausibility test.
With 2 minutes research you can find many studies showing how exercise raises the daily resting metabolic rate of sedentary people, and raises it further for non-sedentary people who add exercise.
For example, I've run every day for the last year, between 5 and 12 km. I eat more than I did when I ran 2X a week, and I have not gained weight. I know that I am not a "randomised blind clinical trial" but I observe a lot of other runners every day.
I find it hard to reconcile the claim with the typical physical profile I see of runners every day - those that run further have that typical "marathon" physique. How is that explained? Without exception these runners would be consuming hundreds if not thousands of extra calories on running days, yet they often appear to be losing weight as they train?
In summary, running is no miracle weight-loss cure but it is generally a very effective way to lose weight as a by-product of being fit and active.
Related: The Exact Slow Pace You Must Run and Cycle To Max Fat-Burning > https://medium.com/body-age-buster/the-exact-slow-pace-you-must-run-and-cycle-to-max-fat-burning-e1059c69bb35