Then you are not understanding it. Looking at a map of people not close to power plants would show the same rough picture. People live where people live, of course! But proximity to nuclear power plants has higher incidence of cancer.
What is different about this study that's worthy of a national map is that it's an evaluation of national data, after having first found the discovery on smaller state level datasets.
there is a small problem though, everything in those power-plants is monitored. so there is no radiation increase anywhere to be found.
if it's the pollutants as the Nature paper claims without evidence, then any other industrial plant would also be emitting those. in fact, coal power plants will emit much more. chemical pollutants are no less dangerous than radioactive ones when the radioactive ones are too low to measure (that is not to say that coal power-plants don't produce radioactive pollutants, they do much more than nuclear power plants).
yet their source for this: I wonder why none of these researchers just go and grab soil samples around the nuclear power plant and compare those to random samples from any other industrial installation... since it's such an obvious thing to do they no doubt did this, why isn't it in any of the relevant papers? could it be that the results are against their ideological anti-nuclear project?