Actually the method is described in the article.
As Y chromosomes are only passed from father to son, that would mean that the Y is a record of one’s patrilineage. Genghis Khan died ~750 years ago, so assuming 25 years per generation, you get about 30 men between the present and that period. In more quantitative terms, ~10% of the men who reside within the borders of the Mongol Empire as it was at the death of Genghis Khan may carry his Y chromosome, and so ~0.5% of men in the world, about 16 million individuals alive today, do so.
If you are interested in how accurate this estimate is, note the the words assuming, about, may, symbol ~. Maybe it's too strong to say that this "precise figure" is pulled out of where neither Sun shines nor historical scientific study usually happens, but it's definitely not an accurate figure. The general idea that a big chunk of current world's population is descendants of Genghis Khan is true, but it's as well true for any historical person. Well, not eunuchs, obviously.
Also this... figure... is usually presented as it means something, i.e. that Genghis Khan really got around, like, a lot. And while he did to some extent, if we think about it, there's nothing really impressive here. People have offspring. Offspring have more offspring. Their offspring have even more and so on. That's why population grows. To call this study groundbreaking, like discovermagazine does, is a sure sign of sensationalism.
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