First, The article cites work that intrinsically religious people (i.e., those for whom religion is an end in itself, as opposed to those who are only religious to fit into society - extrinsically) show lower levels of anxiety and depression. I still need to dig out the sources of these claims...
Second, a good animal model for depression, learned helplessness (wikipedia), generates depression by removing operant control from the animals. Humans with depression often describe their feelings as "having no control over their lives". Even flies show a preference for situations in which they are in operant control, demonstrating that operant control is per se rewarding. One of the symptoms of depression is a reduced sex drive.
Third, animals which receive food on a random schedule often tend to repetitively perform behaviors they were accidentally performing before the food was delivered (superstition conditioning). Such effects have often been related to the development of religion in humans.
These pieces of evidence support the hypothesis that religious people are less depressive because they have the illusion they have control over their lives. Since less depressive people have a higher sex drive than more depressive people (on average), religion, on average, will tend to increase the birth rate - a great prerequisite for positive selection . In other words, people who are able to evade depression by finding control over their lives (or the illusion of control) will have more children than people who do not. Thus, religiosity may be a by-product of such selection.