These are not death as in murder, these are a statistical measure called excess death and it is usually very model dependent. I looked a bit into the models for nuclear accidents. There the problem is, that there is just no good data in the relevant range of radiation. We have data from very low doses due to background radiation and for high doses due to accidents, we don't have good data for large scale releases. Either you can do what is suggested for higher acute doses, then you end up with 40 000 dead due to Chernobyl, or you can fit a second order model, then you will end up with something in the order of 10. (Or you do what Greenpeace did and you look at correlations between irradiation and cancer rates in former Soviet oblasts, where you then have some influence of Soviet industry, etc...) And that is if you want to look at catastrophic risk at all. (After all an RMBK had several design flaws, that modern reactors don't have.)

The number basically tells you that according to a specific model, that is hopefully a good approximation of our understanding of the risks, a certain percentage of the death rate should be due to that factor. However I think these numbers carry not much more information than 32 other bits of the same sentence and to really use them you have to look at the specific model and you need to develop an opinion if the model reflects the relevant arguments well.

I don't know how this study does it, but one can make estimates by seeing how death-rates change in places with different levels of coal particulates, particularly over time as coal plants were opened and shuttered.

Alternatively there are studies that correlate various pollutants with respiratory issues, and then compare that with the pollution emitted by coal plants.

Ideally one would make many such estimates, yielding a range that one could have high confidence is close to the truth, similar to how we use multiple methods of dating fossils, and then know something is wrong if there is a large disparity.