Like so many studies, this one just seems to state the obvious. Except that the article does not state that the loss of a relationship is an incredible blow to one's self esteem. Not just that things went wrong, but the person you were with then, now thinks that it's not even worth trying to patch things up. And the longer a relationship has lasted, the harder that will be. I think the thing about "harder for men" is just sexist nonsense. It is harder for some individuals than others, depending on the circumstances and the individual. Generalizing on the basis of gender just plays into the hands of the small minded sub-editor. It tells us nothing.
Although it could be due to the fact that women are more likely to stay in a family setting - they nearly always get custody of the kids. The Dad is simply discarded as unnecessary. Mum still has the family and the home. Dad is now on his own. No wonder he gets depressed.