The upshot of the article is that a 15-year-old boy whose mother had conceived using donor sperm was curious to know who his father was. He sent some cheek cells to an online genealogy DNA-testing service, which gave him information on his Y-chromosome. The Y is passed along from father to son without much change, if any, and so the boy was able to find other users of the service who had the same Y-chromosome. Now, neither one was his father, but they had the same surname. Since his mother had been given the anonymous donor's date of birth, place of birth, and college degree, another online search allowed him to find lists of names who fit those criteria. And only one name shared the surname he had found.
This story has major implications for people in the United States, as the article points out. In the US, most sperm donors are anonymous, and some request to remain so throughout their entire lives. There is a population of men out there who donated sperm as college students, twenty to thirty years ago, and who might suddenly find that the promise of anonymity has been shattered. Quoting from the article, "Many have not told their wives or children and have never considered the implications of having a dozen offspring suddenly wanting to meet them." There is also the distinct possibility that this news might lead to a drop in the number of men willing to donate their sperm.
What fascinates me about this story is that it's another case of different technologies developing at the same time, leading to implications that no one (as far as I know) predicted. It's one thing to predict the Internet. It's another thing to predict DNA testing. But I don't think anyone put them together in science fiction the way this boy did in real life.