Understanding how population age structure shapes COVID-19 burden is crucial for pandemic preparedness, yet common summary measures such as median age ignore key distributional features like skewness, bimodality, and the proportional weight of high-risk cohorts. We extend the PoPStat framework, originally devised to link entire population pyramids with cause-specific mortality by applying it to COVID-19. Using 2019 United Nations World Population Prospects age-sex distributions together with cumulative cases and deaths per million recorded up to 5 May 2023 by Our World in Data, we calculate PoPDivergence (the Kullback-Leibler divergence from an optimised reference pyramid) for 180+ countries and derive PoPStat-COVID19 as the Pearson correlation between that divergence and log-transformed incidence or mortality. Optimisation selects Malta's old-skewed pyramid as the reference, yielding strong negative correlations for cases (r=-0.86, p<0.001, R^2=0.74) and deaths (r=-0.82, p<0.001, R^2=0.67). Sensitivity tests across twenty additional, similarly old-skewed references confirm that these associations are robust to reference choice. Benchmarking against eight standard indicators like gross domestic product per capita, Gini index, Human Development Index, life expectancy at birth, median age, population density, Socio-demographic Index, and Universal Health Coverage Index shows that PoPStat-COVID19 surpasses GDP per capita, median age, population density, and several other traditional measures, and outperforms every comparator for fatality burden. PoPStat-COVID19 therefore provides a concise, distribution-aware scalar for quantifying demographic vulnerability to COVID-19.