Without having read the study and with only the newspaper reporter's interpretation of the study, I would put this in the category of "junk science" or "bad reporting." My opinion is that it's bad reporting.
Nowhere in the story does it say "chasing women causes men to die earlier than females." The study refers to men undertaking risky behaviour and then concludes that "males in many species have been shaped by trade-offs that increase competitive abilities and risk-taking, which, in turn, increase male reproductive success at the expense of health and longevity."
We all know that "competitive activities" increase stress - even exercise -and stress is a significant factor in disease and aging.
Does the study take into account stress, diet, exercise etc. Who knows?
One of the study's author's says that men need to take extra care of themselves less smoking, less drinking and less chasing the girls around town in fast cars. I would suggest that chasing girls around town in fast cars is not something the vast majority of men do not do. So why single this out as the main conclusion of the study?
I'll cut the study's authors some slack and suggest their conclusions have been twisted and taken out of context by the reporter.
