This is result of studies of many elderly people who have maintained an active mental life even as they aged showing they were less likely to suffer from the many psychogeriatric conditions that plagued people of their age. Mental activity is similar to the muscular system with the body being a self-adapting system, what you don’t need tends to degrade with the body focusing on the ones you do need. Muscles that are used frequently tend to have better tone than ones you don’t and people who fail to exercise their brains into their old age would eventually have it degrade as well.
They should also adjust their diet to have more anti-oxidants to keep the cells of the body longer allowing them to stay active for many more years. At an old age, it seems games even on the computer that challenges the mind to keep working will indeed keep it so well into old age.