As important and big as Nintendo was with the NES/Famicom and SNES/Super Famicom I don't think gaming would be anywhere near as big if this had gone through and PlayStation hadn't become a thing.
PlayStation was cool in a way that the others weren't and appealed to different groups then Nintendo. PlayStation appealed more to an older demographic and this can be seen in it's games and marketing (like those Crash commercials and with stuff like Wipeout really connecting with the club generation with it's vibes and music). They grew the scene in a way that they wouldn't have if they partnered with Nintendo.