How is chess good for the human brain?

"Toughest to understand" is entirely subjective, and the best one can do is put games in categories (chess and go are clearly more challenging to understand than tic tac toe for example).

That aside, I see two problems with your line of thinking. Firstly, the question was not "is chess for smart people?", it was "Is chess good for your brain?". Those are two different questions. I think it's quite clear that chess helps improve cognitive ability, and teaches people how to be able to concentrate, calculate, and how to rely on intuition. Most people, like you said, play chess for fun, but that doesn't mean it doesn't have any value in developing skills that can be used in other areas of life.

Secondly, you are correct that chess is not only for smart people, but it is a game that challenges people intellectually (which is part of the appeal of it for me). If you do not wish to face great challenge on the way to improvement, then chess is not the game for you.

What kind of doctor?

Your right, I agree with this 

Those who want to face challenge will be able to succeed greatly. 

Chess is a game that encourages bravery, it makes people take risk. 

That is what a lot of parents think. Chess could be a waste of time if its not getting you anywhere. 

The benefits of chess is overrated. Jigsaw puzzles, Rubiks cubes, Crosswords puzzles are better for the brain. Chess fanaticism leads to insanity.

In other words a player who is a worse player than you. 

yeaa it's good for the brain but if you only play chess and do nothing else your good brain won't have any good use anyway

True, lets just put it as multitasking 

Chess is just good for relaxing and studying 

Would a doctor makes an above average chess player?

I was really struggling for my time to play tournament chess. I played chess to get money in my university student life in Myanmar. Chess clubs hire good chess players for their clubs for club championship tournaments. . One tournaments usually take 7-9 days. If I play 3 to 4 tournaments in a year, I miss classes for 4 weeks - 5 weeks. Later, I chose a different better way to get money during uni life.  My rank was somewhere around top 100-200 I guess. Even top 10 Titled players could not get proper money for their living. It made me hopeless for playing chess.

I had not realised, your question was rhetorical. You answer your own question, as you like.

Probably some law of diminishing returns.  After you memorize a lot and find the BEST solution a draw when playing a good player in a game over 15-minutes, it does seem a little insane. I have only been playing a month or so, and the computer seems to be as good as anyone I will ever play.  So, to me, chess let's me interact with other players around the world, and that's fun.  It feels better to beat someone at chess than at, say, Call of Duty.  And when that endorphin rush runs out, then maybe I'll take a break.  It also depends how old you are, if playing chess stops you from working, etc.....if you are very young or very old, there might be more benefits.  

Unless that chess player is a GM or a famous one, then yes. 

It has more benefits for old people then younger ones. 

Young people need to focus on their doctor career.