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I think there is zero evidence of this. Lots for the opposite effect like the above post mentioned. If kids can get smarter with educational games, why not just get them interested in books, libraries and museums?
Caveat: I develop video games for a living. I wouldn’t say they make your kid smarter, but used in the right way can encourage problem solving and perseverance. As with everything it’s how you use them, they can also be a fun activity for families to play together. While not every game is a violent shooter, I wouldn’t recommend just sticking a child in front of one. There’s a great website for parents which information on different video games, age ratings etc - https://askaboutgames.com/
In most cases it’s the opposite.
It generally has the opposite effect as children then find that they struggle to focus on things that are less stimulating such as school work.