When Does "Tales from the Forbidden Zone: Stone Monkey" (2017) Take Place?
"Planet of the Apes: Tales from the Forbidden Zone: Stone Monkey" is a science fiction short story written by Greg Keyes that released January 24th, 2017. So when is "Stone Monkey" set?
It takes place on the Planet of the Apes universe timeline in the year:
We know this because the phrase "a legend that dates to the time when the accursed cities of man fell", referring to the massive destruction in the comic-book "Revolution on the Planet of the Apes" (2005), which takes place in 1993 AD. So we know it is after 1993 AD. It must also be before the final cataclysmic event of January of 3979 AD, as seen in the film "Beneath the Planet of the Apes" (1970) [and the expanded ]. The use of the words "legend that dates to" means it is probably much closer to 3979 AD than to 1993 AD.

YEAR AD
We know this because the phrase "a legend that dates to the time when the accursed cities of man fell", referring to the massive destruction in the comic-book "Revolution on the Planet of the Apes" (2005), which takes place in 1993 AD. So we know it is after 1993 AD. It must also be before the final cataclysmic event of January of 3979 AD, as seen in the film "Beneath the Planet of the Apes" (1970) [and the expanded ]. The use of the words "legend that dates to" means it is probably much closer to 3979 AD than to 1993 AD.
It is a midway chronological short story in the Planet of the Apes universe.