It's not an error, though tricky and somewhat unclear.
He is assuming that \xi is constant while n and D are variable. For \xi=2, for example, he is considering a case that the hashes calculated are twice the average needed; he then considers what happens when D, and correspondingly n, go to infinity (continuous case). In this case the chance of not finding a block is indeed exp(-2).
So, is there an implicit assumption that n and D are linearly related?
You see, I have no problem with the observation that finding a block has a Poisson distribution. But the "proof" provided as it stands is simply wrong, unless D is a function of n, and \xi is the limit of their ration when n tends to infinity.