ShapeInterface *CircleAsShape = &(ShapeInterface) {
      .Area = (double (*)(void *)) circle_Area
 };

Phooey! Just

  ShapeInterface CircleAsShape = {
      .Area = (double (*)(void *)) circle_Area
  };

then refer to &CircleAsShape.

This is error-prone because of the cast. circle_Area could have the wrong parameters, or the wrong function could be used by accident and it will compile.

Conformance wise, it is undefined behavior: a function that takes a Circle * is being called via a pointer to a function that takes a double *.

You really want the circle_Area to have a Shape * argument.

Firstly:

  double
  shape_Area(Shape *shape)
  {
    return (shape->interface->Area)(shape); // we lose shape->instance here, just shape
  }

Then:

  double circle_Area(Shape *shape)
  {
    Circle *circle = (Circle *) shape->instance;
    ...  
  }

We now have a cast here; but that is now new. The same conversion was being done through the function pointer punning, without a cast (formally undefined in ISO C). Now we have well-defined behavior: the shape->instance pointer is really pointing to a Circle; it is valid to convert that pointer back to a Circle *.

Then we have:

  ShapeInterface CircleAsShape = {
      .Area = circle_Area
  };

So instead of a function pointer cast with undefined behavior, we have a well-defined function pointer treatment, with a correct cast between data pointers.

Another nice thing now is that type-specific implementation like circle_Area has access to the Shape pointer, and can invoke shape operations on it.

  double rectangle_Area(Shape *shape)
  {
    double length = shape_NominalLength(shape);
    double width = shape_NominalWidth(shape);

    return length * width;
  }

Now you can have subtypes of rectangle which have a completely different internal organization, and don't have to reimplement Area; rectangle_Area works for them. E.g. a PNG image could be a kind of rectangle, using rectangle_Area for its Area implementation. It just provides NominalLength and NominalWidth:

  double pngImage_NominalLength(Shape *shape)
  {
     PNGImage *image = (PNGImage *) shape->instance;
     return PNGIMage_width(image);  // PNGImage is an opaque type from some third party lib.
  }

Whereas if rectangle_Area is like this:

  double rectangle_Area(Rectangle *rect)
  {
    return rect->length * rect->width;
  }

that is not possible, even if you're prepared to modify rectangle_Area somehow to try to make it work. It doesn't have access to the shape container to be able to invoke the abstract shape call; there is no way it can work with PNGImage.