The statistical claims in this article are pure nonsense.

To begin with, in the paragraph beginning "Here is a thought experiment...", yes, your expected return at every interval is a 25% gain. The expected return over N trials remains (1.25)^N. It is not true in any sense that "this bet will not accumulate wealth over time because the volatility inherent in the coin flip impedes capital growth". I can't even fathom the error in statistical/mathematical understanding that led to this claim. It reflects badly on the author and the editorial board.

It's impossible to make sense of the errors in the next paragraph without understanding what led to the errors in the previous paragraph.