The study is age-normalized. They looked at excess deaths by age group.
I did not see that in the NBC summation. The study itself states,
Both groups experienced a similar large spike in excess deaths in the winter of 2020-2021. However, in the summer of 2021 — after vaccines were widely available — the Republican excess death rate rose to nearly double that of Democrats, and this gap widened further in the winter of 2021.
Political party affiliation was associated with excess death rates at the individual level during the initial years of the COVID-19 pandemic. Registered Republicans in Florida and Ohio had higher excess death rates than registered Democrats, driven by a large mortality gap in the period after all adults were eligible for vaccines. These results adjust for county-by-age differences in excess deaths during the pandemic, suggesting that there were within-age-bycounty differences in excess death associated with political party affiliation.