The author of that, David A. Plaisted, is not a historian or a professor of history or anything that gives him particular credentials to try to offer any estimation. He's a computer programmer.
But the author's lack of credentials aside, let's let's talk about the problems of the essay itself. There's a lot of problems throughout it, but most of them boil down to one simple issue: The essay relies very strongly, and for the most part uncritically, on assertions made in non-scholarly older works (often 19th century or earlier) that are heavily biased against Catholicism. In contrast, neutral scholarly sources from more recent years are used infrequently. It is not particularly surprising that when one primarily uses such sources, you end up with conclusions of high numbers of deaths because that's the claim so many of those sources are trying to advance to begin with. One might as well try to write an assessment of Donald Trump's presidency based on articles on Mother Jones, or an assessment of Joseph Biden's based on Breitbart articles.
Time prevents me from giving too many examples of what I'm talking about, but I'll point to a few.
Joseph McCabe's work "The Story of Religious Controversy" (McCabe was an atheist, so you can probably guess what he was arguing in the book) is cited for the claim that Spain had a population of thirty million in the tenth century, but it was only twenty two million in McCabe's time. This is used in the essay to posit massive loss of life. The problem is, McCabe offers
no citation whatsoever for this thirty million people living in Spain claim, which seems to be completely wrong.
"Atlas of World Population History" gives an estimate of four million for Spain's population at the time (if you want to include Portugal, you can add 0.6 million). Note that Atlas of World Population History is actually cited elsewhere in the essay, but instead he just took McCabe's unsourced and inaccurate number and made a bunch of calculations based on a totally inaccurate number.
Similarly asserted (without a clear citation) is the claim that "During its rise to power, the Papacy also essentially exterminated the Heruli shortly after 493 A.D., the Vandals soon after 533 A.D., and the Ostrogoths in 554 A.D, all of whom were asserted to hold to the Arian belief." It is unclear how "the Papacy" exterminated them, when the Heruli were defeated by the Lombards, while the Vandals and Ostrogoths were routed by the Byzantines. Essentially any encyclopedia will tell you this; look them up for yourself on Wikipedia or Britannica. To blame the papacy for the Heruli's destruction makes especially little sense, as the ones who actually did it (the Lombards) were themselves Arians,
enemies of the Roman Catholic Church.
Perhaps the source for this inaccurate claim, even if not explicitly cited, is Taylor Bunch's work "The Book of Daniel", as almost right after the above quote the essay says:
""It is reckoned that during the reign of Justinian, Africa lost five millions of inhabitants; thus Arianism was extinguished in that region, not by any enforcement of conformity, but by the extermination of the race which had introduced and professed it. History of the Christian Church, J.C. Robertson, Vol. 1, p. 521."
-- Bunch, Taylor, The Book of Daniel, p. 101.
Of course, the Heruli and the Ostrogoths also undoubtedly numbered in the millions, and were exterminated."
I am not sure if the essay is trying to imply that the five million mentioned here is ascribed to the papacy or not. It doesn't
explicitly say it, but it certainly seems to be implying it, even though the actual person blamed for the five million deaths is Justinian. Whether it is or not, the five million claim here is very dubious. If one looks at J.C. Robertson's work that is being cited, we see where this claim comes from. This comes from a writer named Procopius, or more accurately his work "Secret History". Secret History is an unpublished work by Procopius that is extraordinarily critical of Justinian (some have speculated it may have been written as insurance by Procopius in the possibility Justinian was overthrown, so that Procopius could show the work off to prove he was never loyal to him), and makes that five million claim. The problem is, that comes a few sentences after Procopius says Justinian killed a
trillion people overall (the five million just being a small portion); see
Chapter 18, entitled "How Justinian Killed a Trillion People". Perhaps it is just me, but if a source claims a man killed more people than have actually lived on Earth, I would be extremely cautious trusting any other numbers it makes. So yet again, a claim is just uncritically accepted despite there being real issues with it.
Another case of accepting a claim of a polemical source uncritically is this portion of the essay:
"There is some additional information about the number killed in Europe in the Middle Ages. For this, G. H. Orchard in A Concise History of the Baptists, 1855, chapter 2, section 11 estimates that there were over 3 million persons possessing evangelical views in northern Italy in 1260, and mentions another authority as giving an estimate twice as large. He states that the number eventually "quadrated," which may imply that it became four times as large, that is, 12 million or possibly 24 million persons, whom he calls Anabaptists. Almost all of these were presumably killed in persecutions."
Having looked at the source, Orchard arrives at his number via some dodgy math. First he says that "Perrin estimates their number in 1260, at eight hundred thousand persons." Then he engages in a bunch of speculation in supposing that this was
actually just the number of "communicants" (by which I assume he means churchgoers) and the number of "adherents" (by which I assume he means the number who actually have belief but aren't necessarily active in practicing them) is higher than that, at a ratio of 3-to-1. So he multiplies the number by four and gets 3.2 million (the linked essay's claim of "another authority as giving an estimate twice as large" is not quite accurate--what happens is Orchard refers to someone else who supposes a 7-to-1 ratio and therefore a multiplying of 8, which Orchard changes to 3-to-1 for the purpose of his claims). And thus the essay takes that, "quadrates" it based on Orchard saying that (why Orchard says that is unclear, but it's accepted uncritically by the essay).
Setting aside the obvious speculation used to get a bigger number out of it, what this is all based on--a population of eight hundred thousand in 1260--is false. Perrin in Chapter 2 of Book 2 of "History of the Old Waldenses" (the work cited by Orchard) does give the eight hundred thousand claim, but says it's for the year 1530. This is well after the 1260 that is claimed by G.H. Orchard and the essay, and 1260 date is required for the essay's claims on this number (i.e. that we can consider "almost all of these" to have been killed in persecutions) to work. Especially interesting is that Perrin holds up the eight hundred thousand number as evidence of the group's persistence in the face of
prior persecution, but the essay (due to not bothering to verify the claim) tries to--after coming up with some ways to artificially increase it to 12-24 million--use it as evidence of many deaths
afterwards by supposing that they all died. Sure, part of the problem was G.H. Orchard mixing up what his source said, but perhaps the essay's author shouldn't have uncritically accepted a claim made in a 19th century book that was pushing the now-largely-discredited theory of
baptist successionism? Heck, the essay itself cites Perrin's work elsewhere, so looking it up to verify it was clearly very possible!
Yes, I know this is only a few examples (I could list many more, but this has already taken enough time), but it seems sufficient to establish the recurring problem of the essay you are linking to, it relying so heavily on old biased non-scholarly works and taking their claims as apparent fact, and engaging in its own speculations.