Games in learning are often electronic, but they also rarely can be board games. Many schools in first world countries use games for learning. There are many different types of topics that games can teach. There are many reasons why games are useful for learning.
For example, Literacy Planet has games that improve children's spelling and vocabulary, and the children really enjoy them, so they play more often. Take it from me, a kid (10) who really likes playing the Literacy Planet games.
For example, the website code.org teaches people how to create video games based on clip-on computer code. There are different ways of doing it, like Star Wars and Minecraft. Kids enter the site having no idea how to use code and exit, if not having a complete mastery of code in general, at least having a basic knowledge that they will keep for the rest of their lives. Do you want children to be intelligent?
It gets them interested in the jobs of the future because most of them will be on electronic devices. If children have a positive experience with programs when they are young, by the time they grow up, they will be up for using all the latest technology. This is important because we will need new devices as Earth progresses.
There is no doubt in my mind that gaming is useful for learning because it can help children learn with a sense of fun, using games for learning covers more topics than normal studies and it gets children interested in the jobs of the future.