The title is a bit sensational; the article directly calls out that they are using grip strength as a proxy for overall fitness and day-to-day ability. So, people who have higher fitness have a lower incidence of depression. I'm not really sure this is news.
It could be that those with poor handgrip strength suffer from a number of health maladies. And though an 'association' occurs between handgrips and depression -- the causality of depression is actually from the underlying co-morbidities.
And vice versa, struggled with years and years of depression in the past, and teetering on the edge of it on and off since, whilst having good grip strength.
Same. Dealing with depression for years. Joining a BJJ class taught me I have abnormally strong grip strength for someone who otherwise isn't fit at all.