I don't know the method that Wayne Grudem used. On possible method is Levenshtein Distance, which measures the number of insertions, deletions, and subsitutions needed to convert one text to another. In order to test the method and compare it with the 92% found in the chart, I ran the first chapter of Genesis (without verse numbers) through an online Levenshtein Distance calculator. Genesis 1 is 4222 characters in the Revised Standard Version, which I used as the denominator:
The only real datapoint we can compare is the RSV to ESV changes and the edit distance method produces a similar number to Dr. Grudem's method. From the mention of "60,000 words" in the chart, I expect that it counts the number of inserted, deleted, and substituted words rather than characters. That certainly would speed up the calculation somewhat. (The recursive algorithm I initially tried needed memoization to return results before I ran out of patience.) It would also, presumably, strip out changes in punctuation style.
Comparing NIV and ESV to the King James itself shows that, at least in the first chapter of the Bible, the NIV translators felt more free to stray from the traditional English translations.