What I have often said here, and I repeat again, is that I do not believe brain games improve the biological function of the brain, or overall brain function.
What I think is that the activities of some brain games can carry over to certain tasks that humans can perform day to day.
There are brain games that happen to be very similar to things that we do. And since most people work on computers, the carryover effect is more likely since the games are also on computers.
Let's say that I have to memorize faces. Lumosity's face game could potentially help me.
Let's say I want to get better at typing. I would play a typing game (although not exactly a brain game).
Another example is archery. Archers purportedly mentally rehearse their actions. While not exactly a brain game, this is sort of a mental rehearsal.
You may counter with - these are not brain games! I would agree. My use of brain game is different. I believe a "Brain game" does not actually improve the health of the brain - similar to how bodybuilding does not actually improve the strength of individual muscle fibers. But it conditions the muscular system for a wide range of purposes, some of which are counterproductive to the overall biological health. Bodybuilders do not make good long distance runners, and if they do not do cardio, they may not actually be very healthy if you just measured they cardiovascular health. Yet they are advantaged at a wide range of athletic disciplines.
From working as a professional software engineer, I believe that I can intuitively know that certain brain games help me. At the very least, they are a "mental rehearsal" like in archery. Maybe they are merely stress relief for me. But deep down, I believe that mental games are not given the credit they deserve and that the benefits are waiting to be discovered. Just like how bodybuilders in ancient times did not necessarily know exactly what these exercises did, they just knew from years of experience that these activities helped them.