They mean surviving progeny with his DNA. After 7 generations, most of your descendants are not actually genetically related to you.
By contrast current estimates are that about 0.5% of the world has a y-chromosome descended from a relatively close ancestor of Genghis Khan. (When his horde burst out, both he and his male relatives took advantage of "mating opportunities".)
A side note. His y-chromosome would have benefited more than his other chromosomes since many of his sons, grandsons and other direct male descendants also had good breeding opportunities. Those men had his y-chromosome, but not all of his other chromosomes.
By contrast current estimates are that about 0.5% of the world has a y-chromosome descended from a relatively close ancestor of Genghis Khan. (When his horde burst out, both he and his male relatives took advantage of "mating opportunities".)
See https://en.wikipedia.org/wiki/Descent_from_Genghis_Khan#DNA_... for more.
A side note. His y-chromosome would have benefited more than his other chromosomes since many of his sons, grandsons and other direct male descendants also had good breeding opportunities. Those men had his y-chromosome, but not all of his other chromosomes.