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They have a section discussing why this paper might seem to contradict other studies showing a causal link:

> This outcome seems at odds with findings from randomized controlled trials in clinical and population samples indicating that regular exercise can relieve symptoms in subclinical individuals and in patients diagnosed as having an anxiety or depressive disorder. To understand the different outcomes of both types of study, it is crucial to make a distinction between the effects of prescribed and externally monitored exercise in selected subgroups and the effects of voluntary leisure-time exercise at the population level. Only voluntary leisure-time exercise is influenced by genetic factors, whereas the other type of exercise is environment driven. The absence of causal effects of voluntary exercise on symptoms of anxiety and depression does not imply that manipulation of exercise cannot be used to change such symptoms. It means that a population association, cross-sectional or longitudinal, cannot be used to justify exercise as a treatment without an actual randomized controlled trial. The possible difference in the antidepressant effects of prescribed vs voluntary exercise is consistent with findings from a recent study suggesting that the therapeutic effects of exercise are nonspecific to exercise. The antidepressant effects of exercise may only occur if the exercise is monitored and part of a therapeutic program.

So it sounds like among twins, if one twin naturally exercises more by their own volition, that twin doesn't in general show less depression/anxiety than the other twin, which is evidence against exercise causally reducing depression/anxiety. However it sounds like it may still be that prescribed exercise as an intervention, beyond what an individual would naturally choose to do, and maybe only in conjunction with therapy, could still benefit an individual (and perhaps then only individuals with clinical symptoms).

This study also does help by showing how the associative inverse relationship between exercise and depression in the general population seems to be from genetics influencing exercise, and not the other way around, and the important of a randomized control trial on exercise as an intervention.