It took me an embarrassingly long time to realize this wasn’t about exercising.

I think it would be better if it were about exercising; it's more useful advise that way.

So, all it takes is for you to work out: You may not get into that grad school / that job, but you'll be healthier and you'll feel less depressed. In fact, even if you're in grad school, it's pretty good advice for coping avoiding burnout, coping with impostor syndrome etc.