Hi, Nivek. I guessed that the biggest immediate effect would be on Star Fox 64. A game following Star Fox 2 and more closely involving Argonaut is more likely to be a sequel than a reboot, as they now have an expanded world to match up to (like the two additions to Star Fox Team, Fay and Miyu) and Argonaut, likely to want to defend their additions to the game, would have a bigger stake in the game/series compared to Miyamoto. This could lead to Star Fox 64 being bigger and take longer to develop, released for the holiday season of 1997 instead of the summer, or even delayed to 1998.
How might this affect Miyamoto's decision to suggest to Rare that Dinosaur Planet should be a Star Fox game? At this point, Argonaut would've/could've been seen as 'the' team that developed Star Fox, in the same way that Rare was the guys behind Donkey Kong Country, with relations with Nintendo still going strong. Here, there's less reason for another team to work on Star Fox, so Rare might be left to work on their game, releasing Dinosaur Planet as an N64 game. I'm not sure if this would butterfly away the Microsoft purchase of Rare, or if Rare would avoid the rather ignoble fall from glory by staying with Nintendo or would burn out anyway, but a Rare making games for the GameCube and Wii (IMO superior to the Kinect as a game system) would be a pretty big impact for one game to have.