It seems there is more evidence to support the notion that puzzles and brain training games do not prevent dementia. Additional support for the ineffectiveness of such games at preventing dementia was published in a recent edition of BMJ. There is a silver lining though for people who like mentally stimulating games — they achieve a higher level of abilities from which to decline.
This study is really more about people who engage mentally in a variety of activities and brain training puzzles may be only a part of that. They looked at people who engaged in tasks such as reading, problem-solving, abstract tasks, and intellectual curiosity. The brain training part comes in under problem-solving.
The take away for me is that it is good to keep your brain active in a variety of ways. This may not alter the trajectory of mental decline, but may give you a higher starting point from which to decline.
https://www.bmj.com/content/363/bmj.k4925