The study, if you read it is mostly based on NY data. It specifically states as much in the limitations:
> this study may not be generalizable outside of the State of New York.
I personally think the study should have published the raw data as well as the aggregate data.
But the study seems to be quite open about it's limitations, listing one particularly limitation which to me is the greatest one if you want to critique the study:
> We are therefore unable to adjust for the possibility that unionized health care workers may transfer residents to hospitals earlier and thereby reduce their facility’s COVID-19 mortality rate.