I originally wrote this as an e-mail to a podcast which was revising its list of the 100 most influential games and taking listener feedback in consideration. Ultimately, a number of messages were not read on-air due to time constraints, and none of what I brought up was addressed on the episode.
Its a topic I'm very invested in, so I ended up going too hard (the below is a revision, the original was over 1700 words); and its all history that hasn't been properly synthesized in English anyway, so I get it. Some of my guidance on this matter came from the GameStaff wiki, which hosts a comprehensive list of every development team under both Square and Square Enix. But the go-to expert on that company history is Ryo Saito. What you read below cribs a fair amount from their researching and mapping of this stuff.