John Philip Quinn was a Chicago-based cheater who wrote self-aggrandising books preaching about the evils of gambling and "exhuming some antiquated moss-covered ruses" used by gamblers. He certainly fits the bill of "whining, mealy-mouthed pretensions of piety" and "terrific denunciation of former associates" to which Erdnase refers. In addition, we know from his own book
Fools of Fortune that he had beef with some of the gambling community in his Chicago (where, of course,
The Expert at the Card Table was published). If you read Quinn's work, he not only names (genuine) names of some of the biggest people on the scene in Chicago at the time, but he also implies that all cheating is done with gaffs and the manipulative skill of the cheater is minimal. Added to this, from David Ben's biography of Dai Vernon we learn that "Quinn was not so reformed after all" as he tried to get into a poker game when he visited Vernon's home town.
My opinion is that Erdnase wrote his book almost as a direct rebuttal to Quinn.