Phrases like "regression to the mean" and "law of averages" are made up phrases typically used by people who are extremely limited mathematically. They don't appear in any textbook. For "regression to the mean" to have any possible meaning, one has to define what "mean" one is talking about, and the sense in which one "regresses" to it.
What I think people think they mean when they say something like this is the "law of large numbers," where the *mean* approaches some true value after a large number of trials. The law of large numbers does nothing to help predict a single outcome, such as the performance in a single game.
This article is complete utter nonsense.