Correlation != Causation
Could the causation conceivably run the other direction? People with beginning dementia exercise less? Yes, that is quite conceivable actually.
Could there be a common cause explaining both? Yes, if you are in good health, with good genes, a good job, leisure time and money, then probably you are the type of person who'll live longer, sport more, and be cognitively healthy for a longer time. It doesn't mean the causality runs in the other direction.
In other words, this study shows what we all know. The 'good' people have all the good stuff. But what we want to know, will an intervention that causes people to exercise more do any good?