Does anyone still read this stuff?
The Russian formalist movement may have only been around for a couple of decades, but narrative theory has kept on growing. Since the late 80s, especially, it has widened its focus to the extent that you can now talk about "postclassical narratology" if you really want to. Given that narratives play a role in so many kinds of texts (written, spoken, and visual), it's no wonder that this is the case. In fact, narratology has become popular across so many fields that people speak of a "narrative turn"—that is, a move towards a widespread interest in the concept of narrative—in critical theory.
Even within the field of literature, narratology has branched out. This has been deliberate on the part of folks studying areas of literature that don't always get much cred in academia; after all, not everyone had been thrilled with the sometimes narrow focus of narrative theory. People working with children's literature, for example, were fed up with narratologists ignoring the value of this sort of writing, so they set about a) highlighting its value and b) analyzing such texts from a narratological perspective.
In the same way that these theorists have drawn attention to children's literature, feminist academics have dedicated themselves to exploring different types of narrative and bringing cultural and social issues into the mix. If you think about binary oppositions, for example, you'll find that even though they play a big role in human society, they're not always balanced: people and characteristics often get lumped into either/or categories, with one side being seen as superior.
So for that reason, feminist theorists often look for these binaries in narratives and then think about how they relate to social roles and inequalities. Male/female, anyone? Gender is a big focus here, but studies have now started to consider issues like race, sexuality, and class, too.
Unnatural narratives are likewise receiving a lot more attention these days, and it's no surprise. Once earlier theorists had established the conventions of various types of literature, it makes sense that later theorists would start looking at the texts that don't conform to the model.
One of the more recent varieties of unnatural text is the "hypertext." You know what a hypertext is: it's like when you click on hyperlinks, going from one webpage to another. From a narrative standpoint, it's hardly a straightforward A→B→C experience. Non-linear texts existed long before the internet, but the internet took this to the next level, with some writers testing out its possibilities for bringing unnatural narratives to life. Check out Shelley Jackson's Frankenstein-inspired Patchwork Girl, for example.
So, yeah, narratology's formalist and structuralist origins have been challenged in recent years, but it's not like we can talk about narrative without paying some attention to structure. What theorists have argued isn't that we should ignore structure but that we should think about it in relation to other factors and take a more flexible approach.
It's also important to recognize that modern narratology comes in at least 39 flavors (give or take a few) and is always changing and growing. Cognitive narratology, for instance, is influenced by research on human intelligence, and who knows what's next? Finally, while narratology has become a global obsession (do we exaggerate?), some theorists suggest that this will probably become offset by studies that have a narrower, more local focus. So watch this space…