I think you misread (or didn't read the entire article). The article states that the majority of the "branches" will live as long as humanity itself. I am currently childless and did not find this a consoling thought (quoted from the article):

"In fact about 80% of the people at that time in the past will be the ancestors of everyone in the present. The remaining 20% are those who have had no children, or whose children have had no children, and so on - in other words, people who were genetic dead-ends. [...] A few thousand years after that, 80% of us (those who leave children who in turn leave children, and so on) will be ancestors of all humanity. What an inheritance!"

No, it is true that eventually most branches will end. It's just on the timespan of 3000 years, 80% of the population will likely be a common ancestor. But if you extrapolate back far enough, there will be one and only one. The only way branches can survive forever is if you assume that all genes have essentially the same chances of survival. This obviously isn't true. Even the smallest enhancement will quickly spread throughout the population.

I am curious when the most recent unique common ancestor of humanity existed. Would we consider him human now or something in between?