The end result of the detailed calculation is that 15 servers are required.
Then in the next paragraph they basically say this isn’t a great estimate followed by this:
Therefore, we approximate the number of servers by depicting how many clients a server handles on a given day:
That formula gives a result of 62500, but it doesn’t make sense to me for reasons as explained in my original post and it doesn’t agree at all to the detailed calculation (which appears at face value to be a much better one, even though the result feels intuitively too low).