The story can be viewed as being important in American literature because it is an excellent example of Poe's theory of the short story, which he explained in detail in an essay. In addition to being a short story writer and poet, Poe was also a noted literary critic of his day; his literary criticisms, especially in regard to short story writing, are still recognized for their merit. Here is a passage that discusses Poe's role in influencing criticism in modern American literature:
Poe, moreover, judged others by these same standards [his theory of short story writing]. By doing so, he is establishing the rules and methods common to New Criticism, the leading school of literary analysis in the twentieth century with its insistence that the text must be interpreted as a self-contained unit apart from the critic's opinions of its author or the suitability of its themes.
Also, gothic literature was gaining prominence in American literature in the nineteenth century, largely as an outgrowth of Romanticism. Poe stands as the most noted American writer of the gothic tale. "The Masque of the Red Death" is certainly one of his most famous. Others include "The Pit and the Pendulum," "The Fall of the House of Usher," and "The Cask of Amontillado," to name only three of the most well known.
So, "The Masque of the Red Death" is important in American literature because it exemplifies Poe's short story theory and gothic writing at its best. Here is a quote from an enotes source on gothic literature that states that Poe's gothic writing, in fact, has influenced contemporary American literature:
Poe is particularly important to the ongoing influence of the Gothic on contemporary literature, moving the genre from an external to an internal focus.
This quotation refers to Poe's focus on character development in his stories, in addition to including the common elements of gothic writing.