I don't think the question is whether games _can_ improve mental health, but whether the opportunity cost is activities that are dramatically better to this end (ie, exercise, going outside, or socializing).
Getting an IV is a dramatically more effective way of hydration than drinking a glass of orange juice. Yet life isn't an RPG where you minmax and pick the task that increases your stat the most.
I didn't mean to imply that rationally optimizing your decisions is a bad idea. Just that things are deeper and more complex.
Exercising might improve your mental health more than playing a video game for the same duration, but both activities will also affect many other "character stats" in various different ways.