They are just selling fun puzzles. What you see is what you get. Even if you wrongly believe that puzzles have some benefit they do not, you don't have to buy puzzle from them; the false belief applies to all puzzles you can get anywhere, including free sources: Internet, library books, ...

There seems to be evidence that mental activity saves off cognitive decline --- just not that it can cure Alzheimer's and such.

http://www.sciencedaily.com/releases/2010/03/100302151242.ht...

http://healthland.time.com/2013/04/15/mental-exercises-are-m...

https://www.psychologytoday.com/blog/the-athletes-way/201403... (#6 - brain training games)

http://www.newsmax.com/Health/Health-News/mental-activity-de...

http://www.healthcentral.com/alzheimers/c/42/151976/exercisi...