Let's suppose that all of these pieces make it through production. Here are some of the added challenges for the writer:
1. The biggest one is that every puzzle piece has to be able to stand alone. So puzzle piece really isn't the right metaphor. I'm not quite sure what would be. Supposing that it wasn't strictly a puzzle, a rubix cube is the first image that comes to mind. Every color dot is a story told in a different medium, but they all occur in the same "world," and you get to pick how they line up. It's most akin to the relationship of a single myth and a larger mythology -- and maybe in this you can see a hint of why I've been so obsessed with mythology and narrative, all my life. Of course, each story will be further enriched, even deepened, when the audience is aware of the bigger picture. But that cannot be necessary.
2. The second challenge is that for a transmedia narrative to be transmedia, you need to able to work in multiple mediums. Even if you're directing other creatives that are working off your script, the more you know about how that medium works, the better.
Now I can get to the point of this post: once all of these pieces are put in place, you as the audience have the ability to not only create one story in your mind, but you get to pick which piece you take in first. You get to fill in the gaps between them, just like your mind fills in the action when you read a comic script. Panels of flat images come to life in your head. So too a transmedia narrative composed of multiple sub-stories.
You may not be inventing the larger arcs, but you are able to interact with them in a non-linear manner. It's a step in the direction toward truly immersive storytelling, which is I think where all of us storyweavers want to go...