Why is Thousand and One Nights referenced in this short story? What is this an example of?

Anton Chekhov's Thousand and One Nights is openly referenced in Jorge Luis Borges' "The Garden of Forking Paths." Albert, a doctor, references Checkhov's story when considering "how a book could be infinite." The circumstances which allow this question to arise has to do with Tu'is Pen's decision to forgo all else in life but writing a book and creating a labyrinth. As Albert discusses Tu'is fate, he brings up the idea of the symbolism associated with a labyrinth. A labyrinth possesses numerous paths: some which lead to nowhere, some which lead to somewhere, and some which lead back to the beginning. By referencing Checkhov's text, Albert comes to terms with the idea that some paths lead one back to where he or she began, in a never-ending loop.
Albert states that he used to not understand how the last page of a text could infinitely lead back to the first, which brings him to ponder the text in question in the first place.

I recalled, too, the night in the middle of The Thousand and One Nights when Queen Scheherezade, through a magical mistake on the part of her copyist, started to tell the story of The Thousand and One Nights, with the risk of again arriving at the night upon which she will relate it, and thus on to infinity.

Here, Albert reflects more than just upon the story. In fact, by recalling the story, Albert stumbles upon an epiphany: lives, like the stories, are linked by time, which repeats itself, over and over again.
Borges' use of the story within his own, essentially, acts as an allusion. An allusion is when one text references something in passing, or indirectly, so as to bring something to mind for the reader. That said, this does not function as a true allusion because the use of the text is actually explained by one of the characters, and it is referenced directly.
The only thing I can say concretely is that the mentioning of Checkhov's text in the short story functions as a reference (which is defined as the act of mentioning something).