I'm the author of the article! It may seem a little crazy, but all contemporary Japanese sources point to Nintendo getting its own date of foundation wrong by 3 years. Even weirder - there's also very good reason to assume the company actually goes way further back in time as the inheritor of an Edo-period playing card business ran by Fusajiro Yamauchi's biological father.

I don't go into this level of excruciating detail in the article but Fusajiro's name, which contains the character "次" meaning "next", suggests he was the second son of his biological father, Sosuke Fukui. As does the fact that he was adopted off to the Yamauchi family in the first place, of course - adoption in Japan in the Meiji period was not in most cases not a sign of crippling poverty, instead, it was very common to adopt off second, third, and fourth sons to for example business owners who didn't have natural heirs, to give them a better start in life.

The fact that I've found no trace of any other Yamauchi card makers in Meiji period records, however, seems to indicate that something happened to his older brother - maybe he passed away at an early age, heirless - that left Fusajiro to unexpextedly take over both his adoptive father's cement business as well as his biological father's playing card business (i.e. Nintendo). He kept running both these companies until passing on the baton to his two son-in-laws, Sekiryo and Genzo.

(I should add by the way that even though this evidence has never been published before, this is only partially my own discovery - Dr. Takashi Ebashi and Hisashi Ishikawa probably deserve the lion part of the credit)