Basically what my title says, is the Narya in Peter Jackson's movies the official Narya or would it be considered... what's it called... Artistic license?
When translating a written work to a visual one, there's always artistic license involved, since the change of medium necessarily requires changes.
In the case of the Lord of the Rings, there has been a considerable body of artwork created since the book was published, with some prominent artists - like John Howe, Alan Lee or Ted Nasmith - considered, if not "official" or "canonical", than at least a commonly accepted vision of how things should look, and were a big inspiration for Jackson when designing the visual look for his movies.
However, as far as I could find, none of them have ever drawn a detailed study of the Three Rings. Even the few scenes where the rings are prominently displayed, when drawn, seem to leave that detail out:
Gandalf now wore openly upon his hand the Third Ring, Narya the Great, and the stone upon it was red as fire
(LotR, book VI, ch.9 "The Grey Havens").
So this is pretty much all the description we have of the ring in LotR. The Silmarillion adds only another name ("The Ring of Fire") and the stone (Ruby).
So Peter Jackson pretty much had free rein to choose how the ring should look.