He addressed that in the third footnote.

Or there might be some hidden third factor, a gene which causes both fat and non-exercise. By Occam's Razor this is more complicated and its probability is penalized accordingly, but we can't actually rule it out. It is obviously impossible to do the converse experiment where half the subjects are randomly assigned lower weights, since there's no known intervention which can cause weight loss.

The model assumes that those are the only relevant variables. Given that assumption, we can prove that weight causes exercise. And that it can't be the other way around.

If there are unobserved variables, it's possible that they can cause weight and cause exercise. However that wasn't one of the hypotheses anyone believed beforehand; they were arguing whether weight causes exercise or if exercise causes weight.

Second, even if there is an unobserved variable, it still suggests that exercising more will not improve your weight. Otherwise internet use would correlate with weight. Because internet use affects exercise. If exercise affected weight at all, then internet use would indirectly cause weight gain, and therefore correlate with it.

The whole point of the article is about this trick. Where taking a weird and unrelated variable like internet use, lets us discover the direction of causation. Which according to common knowledge about statistics, shouldn't be possible. Not without randomized controlled experiments.