On page 74 Stine talks about his 31 page copy of the Star Trek writers' guide, which was obviously an edition issued sometime before his article was published in February 1968.
If it's 31 pages, then it's the Third Revision from April 17, 1967, the most familiar version.
"The time period of "Star Trek" is about two hundred years hence."
And if that is taken from the writers' guide, then writers were instructed by the guide to write details consistent with TOS being about 200 years in the future whenever they included details that would imply when TOS happens.
That's misunderstanding the purpose of a writers' guide. It's not an absolute stricture on writers, just a starting point for their creativity. It's about laying forth the basics of the show's world and characters so freelancers can develop appropriate pitches, but it's meant to inspire their imaginations, not shackle them, so anything it states beyond what's already onscreen is merely a suggestion, to be used if a writer wishes and ignored if the writer comes up with something better. (For instance, the TNG writer's guide's premise that Data was built by advanced aliens was thrown out the window in favor of "Datalore.")
The guide does say on p. 25 that the show is "about two hundred years from now," but this was just in reference to what "Tomorrow is Yesterday" and "Space Seed" had asserted, and didn't stop "Metamorphosis" from implying a longer interval (since Cochrane had been born 235 years earlier) or The Making of Star Trek from asserting a 23rd-century date which the movies then canonized.
Anyway, I'd really be curious to hear more about other aspects of this article besides the chronology question.
Blish used 40 Eridani as the location of Vulcan in Star Trek 1 (1967). Specifically in his adaptation of "Balance of Terror." I believe he was first.
Ah, so that must be where Stine got it. Just to clarify, an Analog issue with a February 1968 cover date would probably have gone on sale in November '67, if the lead time was the same then as it tends to be these days. (Magazine cover dates are basically "display until" dates, typically 3-4 months after release.) The first Blish volume with "Balance" in it has a pub date of January '67, meaning it probably hit shelves in December '66, and Stine obviously wrote his article after April '67 when the Third Revision came out. (I wonder how he got his copy. Was he invited to pitch for the show, or was he friends with one of the writers?)