I've experienced what this guy has experienced. I don't think that's unique. Being an athlete who gets injured and has mental health suffer because they lose their sense of identity and purpose is not anywhere near the same thing as clinical depression. It's a poor term in a way. You can be depressed or feel depressed and those are perfectly legitimate uses of the term, but it's not "depression," not in the same way. It's closer to grief. It's a response to loss.

In any case, I'm not exactly up to date on the state of the art in terms of standard of care, but as far as I understood the role of a psychiatrist, it is specifically to write prescriptions. Exercise is not a controlled substance. You don't need a prescription to do it. Any doctor or even just a clinical therapist, counselor, anyone with a license to listen to you and make recommendations, can recommend exercise. And I'm sure they do. If you make it to a psychiatrist, it's because the less controlled options didn't do the trick.