I don't think you can use wikipedia as a reliable source in a discussion. Either way, mini-games can be plot-related but in the end they're not the main genre.
In the end, VNs are more of a way of telling a story, like movies and books. You can add lore in scrolls/books/reading in general in a game (Dark Souls; Lords of the Fallen), and you can also add movies (cutscenes). In the same fashion, you can add something using the VN style to your game, but it's still a video-game, not a visual novel. Still, it's still a young medium and it'll develop with time, that's for sure. Well, I honestly don't really understand most of your arguments so I might be interpreting what you're saying in a really wrong way.