The author does say that the Parrondo's paradox only works if the games are not independent. It still is paradoxal that "A combination of losing strategies becomes a winning strategy".
It's only 'paradoxical' when the details of the games are sufficiently obscured.
If you word it as "a combination of losing strategies becomes a winning strategy" many people will be surprised and ask you to explain.
If you word it as "losing in A adds to the prize in B, so playing both beats the house" people aren't going to be impressed. note: used a simpler A/B mechanic than the blog post for illustration purposes
That's what "paradox" is: when a simple model or explanation seems to show a contradiction, and a more sophisticated model is needed to understand the situation.
But in this case the 'simple model' is less 'simple' and more 'misleading'. Something should be a paradox without trickery. Someone hiding invalid division to make 1=2 is not a paradox. "Set of sets that don't contain themselves" is a paradox.
