Games teach you how to learn.
Games create simulated worlds, either by showing them to you or through a set of abstract rules and/or physical props, organise the players towards a specific goal or set of goals, that encourage the players to learn the rules of the game world and skill themselves in the specific way the game requires, and then use the newly acquired knowledge and skill sets to pass levels and gain a sense of progression. In other words education and training.
That’s why games make you smarter. Game skills are absolutely transferable to real world tasks. Plenty of groups are already creating games that train people in useful skills. The frigging US Army uses a video game to simultaneously attract and train potential recruits.
Games can be both very fun and very powerful tools. The trick I think is that the more we can make game tasks mirror real life tasks (without ruining the fun) the smarter those games will make us.