Three Levels of Analysis in Transmedia Narratology

When moving a story from one medium to another there seems to be 3 areas (or levels?) to focus on.

1. Is the original author's style preserved?
2. Are the particular aspects of original genre preserved?
3. Is the story preserved?

There appears to be 3 levels of analysis (author, genre, story)

In game studies, it appears that the focus is on level 3.  But, what about genre characteristics and author style?

Of course, this is assuming that the goal is to preserve characteristics of the original.