Ok, I skimmed through the article, and I am puzzled first and foremost about its purpose.
People who deal with stats on a regular basis don't believe that all distributions are normal, so that is not the target. Consider queues, such as the queue for a bank teller or grocery cashier. It's well understood that an exponential distribution provides a good approximation for the time between people joining the queue. Stock returns are well known to approximate a log-normal distribution but with kurtosis (fat tails).
Ok, now I saw the top of the article and saw that it was published in Psychology Today. The PhDs in the subject are hopefully proficient in statistics, so I will generously speculate that the purpose of this article is to inform the practitioners that are less math savvy. It's just not groundbreaking research.
