It's not clear what the map represents. It appears that the map represents TOTAL cases per unit area, not cases per some number of people.
Of course there would be more TOTAL cases in densely populated areas. And the more rural states, e.g. in the South, would naturally have fewer TOTAL cases and fewer cases per unit area, even if they have more cases per capita than other states.
The most relevant statistics are in the two columns "per 100,000 people" below the map.
Other factors being equal, one would expect states containing densely populated cities, such as NYC, to have both more total cases and more deaths per 100,000 people than the more rural states, because COVID is most likely to be transmitted in big crowds, which there are more of in large cities.
The states with the highest number of deaths per 100,000 residents are Mississippi (342), Alabama (326), New Jersey (317), Louisiana (316), Arizona (297), Oklahoma (294), New York (293), Arkansas (284), and Florida (283).
Mississippi, Alabama, Louisiana, Oklahoma, Arkansas, and Florida are all in the sparsely populated South, so their presence in the top nine clearly indicates they are doing something wrong.
New York's and New Jersey's presence in the top nine is no surprise, given how densely populated we are. But what IS a surprise, looking at the map, is that these cases are NOT concentrated in the NYC metro area. On the contrary, they are concentrated in some of the more right-wing parts of each state.
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