It is a very interesting and complex question. The most important part of it is probably in the word "people". How would you define such a thing as a "people"?

Some philosophers and historians have answers for us here. French philosopher Paul Ricœur defines identity as a two-pronged phenomenon, first there is what we are not, which he calls identity-ipse, or ipseity. Anthropologists have a nice word for it too, they call this propriety of human groups to define themselves by referring to another opposing group schismogenesis.

This part of identity isn't where literary texts are the most at stake, but Ricœur tells us, secondly, that identity is also defined by what we are, which seems a bit obvious, but isn't. Think about it: how can you tell that there is a continuity between us this morning and us at the moment? It is even more complex for human groups, since all the members of a given "people" that existed 150-200 years ago are long dead. How can this people have an existence over time? How can it be the same people now that it was two centuries ago since absolutely no member of the group has survived?

Ricœur has an elegant answer in order to explain what he calls identity-idem or sameness, he calls this answer "narrative identity". The way to connect the dots between you 10 years ago, you this morning and you now is a narrative. The same goes for a "people". Narratives play a huge part in building collective identities over time, to tell the story of what they were, where they come from, and even where they are going.

An important historian, Benedict Anderson, came with a similar answer for explaining the modern phenomenon of nationalism. For Anderson, the invention of the printing press has played a huge role in building national narratives through the diffusion of national languages and stories. Soon enough, these narratives would be ingrained in the building of nationhood through education systems.

So, to give an answer to your question : What makes a work/retelling of history into a cornerstone of a culture? It is not in the characteristics of the work itself so much as in the function it plays in cementing a narrative identity.

If we take The Illiad, for example, it became important in Greek culture as it served a useful narrative for the unification of the Greek peninsula. It retold the story of how all the Greek tribes united under Agamemnon to fight a common enemy. This would be taught to young Athenian aristocrats, which would in turn serve as the culprits for Roman education.

The Romans would go a long stretch in trying to paint themselves as the rightful heirs of Greek wisdom, so they would also be maintaining the text alive, even though they created an Odyssey of their own under Cæsar Augustus, The Æneid. Of course, several Western powers, from Charlemagne's Empire to the Kingdom of Prussia, would continue to claim themselves as rightful heirs of Greece or Rome, copying, diffusing and teaching these stories over the centuries.

These cases, though, are a bit more obvious, as they are Epics, akin to the modern Hollywoodian retellings of semi-historical semi-fantasized events, but we have some weirder cases. One of them is Don Quixote, which became the bona fide national novel of Spain while it is an erudite criticism of medieval chivalry novels. Another one is Dante's Divine Comedy, which has nothing to do intrinsically with Italian Nation building (there was no such thing as Italy in Dante's time).

Both these works have in common that they were both popular and written in the language that was put forward by the institutions of these emerging states. In the case of Italy, the Italian language was almost built from the ground up using the Fiorentine dialect in Dante's Divine Comedy. This was in turn taught in schools all over the peninsula after unification.

New World states would have another problem: how can you call yourself a distinct "people" when you don't have your own literature? A narrative of your own? This would lead to an almost mad search for the Great American novel or the Great Canadian novel, the one that could confirm these colonial outposts weren't just badly implanted Europeans on another continent, but legit and distinct peoples. Last of the Mohicans? Moby Dick? Which book could serve as the one to impose on any student to convey the image of the nation?

In order to make such a book a "cornerstone", it has to have a lot more than to be a "good story", it can be because it is one written in a specific language, one telling a narrative that suits the idea authorities want to convey of a given people at a specific time, one that has international impact and can tell how great the said people is... There are many reasons, but these reasons are nothing without the institutions to back them: imagine how many copies of the Illiad people had to make in order for the text to reach us ? There are plenty of Epics, think about the Hollywood peplums, or a movie like Gone With The Wind which retells a national narrative of American reconciliation... Why not them?

Because our cultures remain text-based. This huge amount of energy invested in a single story is testament to the institutions needed to build collective narratives: schools, teachers, politicians, printers and so on, all the way to the Modern State : printing, diffusion, training of teachers. All this is made possible because there is a sense of collective belonging that results in State organization, this belonging in turn being conveyed by narratives that help cement the State, and so it turns and perpetuates over time...