First, thanks for bringing up the article. It is probably part of the
inspiration for PoFV's story, just as Touhou's sixty-year cycle of three lights, four seasons and five elements is inspired by the real life
cycle of 60, but they are otherwise entirely invented by ZUN.
Most Touhou stories do in fact happen around the time of their release. For games, this means happening in the same year, with exception of some spinoffs.
(The real purpose of introducing the cycle in PoFV is to talk about WW2. Like some things in Touhou, it's actually better to not take it at face value.)
Also, the description provided by your article is very shallow. The real cycle of 60 is a synthesis of two ancient Chinese systems, the Ten Heavenly Stems and the Twelve Earthly Branches, both dating back to Shang dynasty, older than the ideas of five elements and twelve animals.
Of course, when Japan adopted the cycle, the Stems and Branches have already been prominently associated with the five elements and twelve animals. So in Japanese on-yomi reading, they are pronounced using
these names. The Heavenly Stems are all named in the format of "Elder Brother of Metal", "Little Brother of Metal". If you are seriously going to translate in this way what that article refers to as "Fire Horse", 丙午 Hinoeuma, it should be "Big-Fire Horse", because there is also a "Little-Fire Horse"!