There's a specific, somewhat uncommon word I have in mind. I came across it some time ago, but I can't remember it and can't find it back. It perfectly, succinctly represents what I'm about to describe. Also, it's not edutainment.
The word is one you would use to describe a novel/game/movie/whatever which, as an accessory to its primary goal of entertaining the audience, also seeks to educate the audience about specific topics.
For example, imagine a political thriller where the audience comes away with some understanding of the inner workings of the U.S. senate. Or imagine a work of historical fiction that greatly deepens the audience's understanding of a particular aspect of the Korean War. Or a novel where the protagonist is a sumo wrestler, and the audience comes to learn a great deal about sumo culture as a byproduct of the storytelling.