Yes, as most have said, I think running can be a part of the jig saw leading to good mental health.
Other things I've found hugely helpful is just trying to lead a simpler, ethical life, dealing with my past in a constructive way, being part of a like-minded community, meditation and helping others. I'm a long time sober recovered alcoholic, which is classed as a mental health problem.
I feel pretty well sorted these days - I have good mental health - I'm happy and have a good general sense of well being. As I say, running is part of the jig saw, but I do not think it's the total solution. I've had to do the other stuff that I've listed too.