No gamblers fallacy here. Nakowa was lucky, very lucky, unlikely lucky - if he had played long enough, he would have ended up losing. That's no fallacy, that's math, because you do realize that the house has an edge - right?
The point is that he doesn't have to play long enough to lose. He's demonstrated over and over again that his bankroll is big enough that he can let variance take him into positive territory, and walk away.
The Kelly Criterion applies to situations where the player with the edge can keep betting as long as he likes. With JD, the house has the edge, but can't initiate bets.