Was the guy in the video "proving" anything, or was he just paying with numbers like most other KJVOs and fundies do?

Meanwhile there are countless facts and discoveries to prove the exact opposite - that the KJV is one of the most corrupt translation in existence:

In the Preface to the Revised Standard Version of the bible this notable statement is made regarding the need for a revision of the English translation: "Yet the King James Version has grave defects... was based upon a Greek text that was marred by mistakes, containing the accumulated errors of fourteen centuries of manuscript copying. It was essentially the Greek text of the New Testament as edited by Beza, 1589, who closely followed that published by Erasmus, 1516-1535, which was based upon a few medieval manuscripts. The earliest and best of the eight manuscripts which Erasmus consulted was from the tenth century, and he made the least use of it because it differed most from the commonly received text; Beza had access to two manuscripts of great value dating from the fifth and sixth centuries, but he made very little use of them because they differed from the text published by Erasmus". [...]

With regard to the textual problems of the King James Version, Dr. Tischendorf writes: "…this text (the Received Text) differs in many places from the oldest authorities of the 4th, 5th and 6th centuries, and, therefore, must be replaced by a text which is really drawn from the oldest sources discoverable. The difficulty of finding such a text lies in this that there is a great diversity among these texts." (Codex Sinaiticus; by Dr. C. Tischendorf, p. 85).

Dean John W. Burgon, one of the most respected of scholars, is cited by Dr. David O. Fuller in his book WHICH BIBLE?, when he wrote in reference to Codexes B, Aleph, D, and L: "I insist and am prepared to prove that the text of these two Codexes (B and Aleph) is very nearly the foulest in existence" (Pp. 126-127); and "That they exhibit fabricated texts is demonstratable… B and Aleph are covered all over with blots -- Aleph even more than B.... We suspect that these two manuscripts are indebted for their preservation, solely to their ascertained evil character" (Pg. 93, 128). Burgon then goes on further and states: "No amount of honest copying -- persevered in for any number of centuries -- could possibility have resulted in two such documents" (Pg. 93). Burgon also said: "By far the most depraved text is that exhibited by Codex D" (Pg. 93). [...]

The problem is that believing Christians today have no means to deal with the issue of the corrupted biblical texts, so they have adopted the doctrine that God wrote the Authorized, or King James Version of the Bible. It does not matter that the Authorized Version is founded upon the most corrupted manuscripts in existence. It does not matter to this group of believers that the Authorized Version is at many important points in opposition to the original teachings of Jesus. What matters is that the Authorized Version which was composed in the year 1611, says what they want to hear, and therefore they reason that God must have written it. Thus, what this ultimately means, is that the faithful flock expects God to be in subjection to man, and conform to the doctrines contained in the believer’s version of the Bible. What they in fact proclaim, is that since the church wrote it, then God must accept it!

Whole article here. Note that despite the length of this article, there are much more evidence that were not covered in it. To know about the history of how the KJV came to be, read this article.