The economic growth rate for countries with lower real GDP is greater than that of countries with high real GDP. This is because the low-income nations are increasing their standard of living at a higher rate by copying and using the advanced technologies and institutions built by rich nations over past decades. It helps the low-income nations to grow at a lower cost and time than rich nations.
For example, consider an African with zero internet connectivity. The country wants to bring internet connectivity to its economy. Instead of investing its resources in developing internet facilities in the country through research, it will buy and copy the most advanced and cost-effective internet technology and use it for the economy. In this way, the African country gets the most advanced wireless network at a lower cost and time than rich countries.
Since the countries with low real per capita GDP are increasing the modern economic growth faster than countries with high real per capita GDP, they will reach the living standards of rich countries in the future. Thus, they are not always destined to have lower living standards than countries with a high real GDP per capita.