If JW outlived Stalin, it was because Stalin wasn't interested.
Doesn't necessarily mean Stalin didn't want the Duke dead at one time or the other. But, the life of a dictator being what it is, one crisis drives out the other, and unless it had really, really high national priority (like the Trotsky assasination) it would be eventually forgotten. I think John Wayne was a hard enough target that a casual Stalin remark 'I want him dead', which would have been good enough to finish some poor Russian or even American man-in-the-street, would have been insufficient.
The Duke, after all, had money, the muscle that money can buy, and was on his home turf. Even today, a loser like Saddam Hussein gets considerable protection out of simply hiding in his hometown against a force far greater than Josef Stalin. If he tried hard enough, Stalin could probably do it, but even the predator seeks easy meat.
I don't think the article made any assertion about what kind of priority Stalin assigned the task, so your point is a rather fine one. I do know, as you should, that getting rid of Tito was a top priority for Stalin from 1948 till his death in March 1953, so much so that he staged show trials in other satellite Eastern European countries of various Czech, Romanian, Hungarian and so forth officials on charges of "Titoism"---just as a decade before he had ranking party members "tried" and executed as "Trotskyites." With all this effort and all the priority that getting rid of Tito had for Stalin, Stalin failed to get rid of Tito.
There's much more we know about Stalin and his methods and predilections that make this story believable. For now, it suffices to cite the example of Tito as disproving the canard that "if he really wanted to, Stalin always got his man."