EDIT: I wanted to add that exercise also has a great effect on my mood, but only temporarily. By following a consistent diet that (in my case) is low glycemic and high in protein, the stability of my mood was much greater than exercise alone.
I do not have time to read the whole paper right now, but one question I have about the results is the prescribed exercise. In my experience, the type of exercise I do can have very different affects in how it makes me feel afterwards. For example, my mood is stabilized for much longer if I do 15 minutes of interval sprints rather than a 30 minute run. Cycling will also make me feel much different than high-weight/low-rep weightlifting.
What I am getting at is that if the "exercise" routine was run for 30 minutes 2 time a week, I could easily see how that would not affect depression. However, if it was a regime of HIIT or heavy compound exercises (squat/deadlift/bench), I would be very surprised if people didn't see long term mood benefits.