I’m no expert, and this isn’t going to satisfy an atheist, but here’s my take: I don’t think there’s a problem with accepting that, strictly speaking, there are physical benefits to having sex. His claim that is necessary for mental health, however, is not necessarily correct, and not only that, but intertwined quite intimately with mental health is one’s spiritual health. So claiming that sex has physical benefits, and even acknowledging certain psychological benefits, to the exclusion of the discussion of spiritual effects (i.e. ensuring that these cited physical and psychological benefits are being obtained in a morally acceptable context) is in a certain sense misleading, and in another sense, downright harmful. There’s the objective reality that someone who is misusing the the sexual act outside its objectively correct context is spiritual harming his soul, and therefore any perceived physical or psychological benefit is almost completely, if not just completely, meaningless. Being in a state of mortal sin is very damaging to someone, certainly spiritually but also in many cases psychologically, whether one recognizes it or not.
The physical and psychological benefits of sex cannot be adequately discussed unless one speaks of them occurring within a morally acceptable context.