One interesting thing I've read in NeoGAF, but sadly can't find source materials behind the posts, so take it for what you will, is that Yamauchi wasn't necessarily angry with Square for jumping ship, but for supposedly talking to Enix's president and talking him into moving Dragon Quest VII onto the PS1 from the N64.
I don't see how that could be true since FF was one of the biggest RPG series in the world and probably the biggest on the SNES. I could see the DQ talk making them angrier (if it really happened) but VII's move to PS definitely soured their relationship.
It's possible to depart with a company on amiable terms, but if you poach some of the company's other talent after you leave, you can make a safe bet that any goodwill you had when you left will be gone no matter how amiable the original parting was. At the time, Dragon Quest still made a lot more money for Nintendo than Final Fantasy did. So I can definitely see Yamauchi being disappointed but accepting over Square leaving but going apeshit over the idea that Square took Enix with them.
It would be nice to get some perspective from Yuji Hori (DQ producer) or Keiji Honda (Enix president who still holds an honorary chairmanship at Square Enix) on why Dragon Quest VII was moved beyond the usual speculations of low CD-ROM costs and whatnot. Keeping DQVII would have made things much more evenly balanced between N64 and PS1 in Japan, though it wouldn't have made a difference in the US. At least Nintendo would have had a major RPG to appease US N64 owners who were complaining about N64's almost complete lack of RPGs, and the difference in Japanese sales would have enticed more Japanese devs to stay on board with Nintendo.