Now I am by no means condemning casual sex, but this study, from what you can glean from the linked article, doesn't say that casual sex != emotional damage. It says that the people having casual sex in this sample were not significantly more (or less) emotionally damaged than people who were not engaging in casual sex at the time examined by the study.
It could be the case that some people can't handle casual sex and that's why they stick with committed relationships. The reason why those people can't do casual sex may be based in patriarchy, cultural norms that privilege committed relationships above all, norms that denigrate people who engage in casual sex as sluts or emotionally disconnected players, or something entirely different. But it's no good to say that casual sex is not damaging, because for some people it is. If you can't check your expectations at the door, even the most lighthearted fling can turn fraught and weighty.
I applaud the study insofar as it combats the Laura Sessions Stepp "casual sex is always and everywhere BAD" position, but there's no need to stretch the results to cover more than they can support. Some people are happy having NSA hookups, but others might be better off recognizing that they need to either shed some baggage or refrain from casual sex.