Does one graph explain the huge variations in COVID death rates for different parts of the world?

Those numbers are case fatality rates, which vary tremendously based on the amount of testing. Antibody tests show 5 to 100 times more people have been infected than is indicated by the official cases.

The number of fatalities divided by the total population is good indicator of both the spread of the disease and the seriousness of the infections. A resistant population may prevent transmission. It may also mean that those who have symptoms have milder infections that are less likely to be deadly.