Yep, Nintendo has done a great job of branching out and enticing "non-gamers".
I think part of the reason why writing gets such a low priority in most games is because game developers assume that "Hey, if you're creative enough to program the game, then you must also be creative enough to write the story for it too." But the open world of creative writing is the polar opposite of the constrictive math and logic that is required to make that game in the first place. Each requires a different mindset and it's very rare for someone to be equally gifted in both.
On all the gamedev podcasts I've listened to, I've heard them talk at length about hiring more programmers or composers or artists, but I don't recall them ever saying, "We really needed a better writer." A lot of game companies could easily afford to hire a good writer, but the vast majority of those funds get funneled into the programming, graphics and music.
Going back to your comment about "people who read books often turn their noses up at video games.": I think there are 3 main reasons for this:
1) Unless it's a Choose Your Own Adventure, books are extremely linear experiences. You can read Tolkien's Lord of the Rings a thousand times and Sauron will never win. It's understandable then that readers that *like* linear experiences are less prone to gravitate to games. But that's largely because most people still associate games with lots of choices and multiple endings. If you can create a game with a very linear, one-ending type of story, I think you could have success appealing to that crowd. A visual novel would be an excellent medium for this.
2) Games (and movies) do all the visualizing for you. But although the plot of a book is linear, books give the reader the ultimate freedom in being able to visualize locations and characters according to their interpretation. The more realistic the graphics are in a game, the less freedom the player has in imagining how things look. However, if you keep the graphics simple, you can still allow the player to visualize things according to their taste. An example I like to use is one of my favorite games, Final Fantasy 6. The graphics on that game certainly weren't realistic, and the character movements and animations were very limited, but that very fact gave me the freedom to imagine what it would be like if it were more realistic. I could see the game world as it was presented while simultaneously hold in my mind an idealized, fantasy version of how things would look and behave in real life.
3) Readers like to read, but hardly anybody likes to Re-Read. Yet this is exactly what happens with the vast majority of games. You play a little, get engrossed in the story, then you die. Now you have to suffer through all the same narrative and dialogue you just read all over again (unless the developer was so kind as to permit a Skip button). As an avid reader myself, I think a solution would be to allow for dynamic dialogue and narrative -- but this would take a lot of creative effort to implement well.
Part of the strategy to get readers to play games will be to show readers that games are simply a different medium for telling a story. I think there is growing realization of this as there has been a huge increase in visual novels.