This is actually a myth:
In a way this is a cheap magician's trick, because the only reason people can read the scrambled words is because they aren't very scrambled. Fixing the first and last letters means 2 and 3 letter words don't change at all, and 4 letter words just swap the middle letters. That's the bulk of our vocabulary. Try making a sentence with very long words, and our ability to read words "as a whole" mysteriously vanishes. To wit:
Bblaaesl pryleas pnmrrioefg sllaimy aeoulltsby dvrseee clbrpmaaoe tteenmrat.
is incomprehensible, because now every word is truly scrambled, with the first and last letters being an insignificant proportion of the total.
I think the author of that quote was missing the point, or more likely, was deliberately obscuring it. Nobody would suggest that letter order is irrelevant to written communication, or that the brain can effortlessly descramble any legal English sentence. The real point is that English as it is usually written has enormous redundancy, much of which is provided by short words that provide context for the long ones, which our brains pretty much skim over as a result.
As for the scrambled sentence in the quote, it's a deliberately artificial construction. I've never written anything remotely similar, even in technical research articles. In addition to its rather clumsy phrasing, it's also written so as to have:
1. No words shorter than seven letters
2. None of the ten-hundred most common words that comprise 50% of written English
3. No natural repetitions like "players playing" and "similarly... similarly"
4. Long, vague words ("performing" and "treatment") instead of short, precise ones ("playing" and "pay")
5. The (presumably-accidental) omission of an "i" and an "r" from "sllaimy"
Here's the same sentence, still with the long words and unnatural phrasing, but with some of the short words put back in:
"If two bblaaesl pryleas are pnialyg at a slaiimr leevl, tehn they aeoultsby dvrseee to rvceeie slaiimr pay."
