Sure, playing chess needs intelligence, dedication, and good chess players are smarter than an average person. But it’s waaaay exaggerated in movies. I’m a math researcher, and in any movie, my department will be full of chess geniuses. But in reality, only about 10% of them even play chess.
In my teenage years I really tried to master it well. I score relatively high in chess.com and lichess but I share your sentiment. If you are a chess master it doesnt mean you are super smart it means you are super good at chess.
Science confirms this in a way. Prof Andrew Huberman has a podcast episode about games in general and their effect the brain development and the takeaways: