The problem is that what doesn't work is "strawman exercise": for instance, the kind of exercise that a sedentary volunteer test subject is able to handle in some study.
Before exercise works for fat loss, you have to train up to the intensity and volume that is required. That takes months. Consistent months during which you not only don't give up, but pile on the challenges. If you quit, you lose your progress and slide back to the start.
You can't measure exercise just by the time put in and the theoretical calories, by the way. There is a quality component to it.
Another thing is that once you have a decently low body fat, the remaining areas where fat accumulates on your body will show to be "exercise resistant". It's very hard to get rid of that centimeter of fat from the back of your thigh, calves, upper back and arms, or central abs. Or that pesky "love handle" area. That, I can attest, either can't be done with exercise, or requires exercise to be a full time job. But that's not what this article is about; the claim is that exercise isn't effective against obesity.