What can we conclude from correlation?

This is wrong: "We can conclude that many people become right-handed as they grow older." We cannot conclude this at all from the given data.

For one, the study only takes a sample at one point in time, rather than selecting a sample and monitoring their progress through many decades. This is what would be needed for us to even entertain the possibility that aging causes a change in handedness.

Other possible causes include that left handed people might have a shorter life expectancy, or perhaps there was a spike in the birth rate of right handed people in the past. There are many other possibilities that have been mentioned in others answers which would also account for the skewed proportions without requiring people to change handedness with age, which is what you falsely concluded in the test.

Also, just an observation, but it appears the "study" was conducted under false pretenses. Handedness is a false dichotomy, people can also be ambidextrous.