I think the biggest problem with this utter nonsense is this:
> In other words, one can assume with 95% certainty that any individual human would be within the last 95% of all the humans ever to be born
"any individual human" really means "a human chosen at random" from all humans who will ever live. Then they go on to assume that this is representative of the humans who have already lived. But clearly there's a problem there. They find a statistic that is true of all past-and-future humans and then assumed it must be equally true of all past humans as well. In fact we've exactly chosen the subset (past humans) as those that are least likely for this statistic to apply. It'd be like deriving some statistic about being 95% sure any given human can run a mile within 10 minutes, and then applying that statistic specifically to those humans with no legs. It's that dumb -- clearly past humans are fundamentally different from past-and-future humans in exactly the property they're sampling.
You can easily see this problem by simply going back in time and applying the same argument at any point in history. At some point, the total number of humans who had ever been born was 1 billion. At that point, we would have been 95% sure that the total number of humans would never exceed 20 billion. Oops! In fact, we would have been 99% sure that the total number of humans would never exceed 100 billion. Double oops!
Go back to when the total number of humans who had ever been born was 1 million. We would have been 99.999% sure the total number of humans would never exceed 100 billion. Triple oops!
It's a nonsense argument.