This is disappointing news: Based on a number of experimental studies, brain-training exercises and games don't seem to improve general brain health or ward off dementia.
It is true that practicing specific tasks, such as learning and recalling names or doing math, does improve one's ability to do those tasks. But the improvements don't seem to extend to other mental abilities, even some that might reasonably seem related. Here's a brief video about that, and if you go to the YouTube page you'll find links to the research discussed.
All that said, it's conceivable that doing a wide variety of different mental exercises (say, learning languages, taking classes, reading, traveling, meeting new people, etc) might help more broadly than playing games. And even if they don't they can be worth doing for themselves. That can also be true of games, for that matter.