Accelerated global population aging challenges conventional economic growth paths. Yet, the mechanisms underlying the transition from the age-based demographic dividend, derived from a favorable age support ratio (ASR), to a skill-based dividend, driven by human capital accumulation, remain insufficiently understood. Using population census data for 336 Chinese cities from 2000 to 2020, we develop a task-based skill ratio (TSR) index to quantify the skill composition of local labor markets, capturing the relative intensity of high- and low-skill tasks within city-level employment structures. We identify a divergence trend where the ASR peaked around 2010 and has since declined, while the TSR has continued to rise and diffuse geographically. We further examine a synergistic effect between ASR and TSR on economic growth and project the compensatory TSR required under alternative demographic scenarios to 2100. It shows that both ASR and TSR positively affect the per capita GDP of a city, but the latter plays a dominant role. A higher ASR amplifies the economic returns to TSR, with the old-age support ratio (OSR) as the binding constraint. Projections indicate that delayed retirement can partly alleviate the effects of the ASR decline, but cannot reverse the long-term trend. Continued improvement in the TSR is therefore necessary to offset this structural demographic shift. Economic growth relies less on favorable age structures and increasingly depends on the skill composition of the workforce, making skill upgrading central to sustained prosperity.