Alternative Timeline - after the N64-CD

[The_Liquid_Laser]

Let's be clear.  Microsoft entered the market to "stop Sony".  Bill Gates did not want Sony to have a computer in the living room, which is what the PS3 originally was.
https://www.gamesindustry.biz/articles/2013-02-07-ex-microsoft-vp-xbox-was-to-stop-sony

With that in mind here is how I see each generation playing out:

Generation 5 - Japanese third parties, especially Square, all stay with Nintendo.  Sony still gets Western third party games like Tomb Raider and the GTA series (although the latter will not really be important until generation 6).  Sony also gets EA, because EA has always hated Nintendo and always will.  The Saturn still has the same fate.  In the end Nintendo wins with Sony being a very strong second place.  Nintendo wins Japan and NA, but Sony gains a slight lead in Europe.  Platform totals are something like Nintendo 80m, Sony 55m.

Generation 6 - Microsoft does not enter in generation 6, since Sony didn't win generation 5.  Sega has the same fate with the Dreamcast.  Nintendo decides to have mini-discs again.  This drives a few Japanese third party games to PS2, but not all since the mini-discs have enough space for most third party games.  Meanwhile the PS2 is still a DVD player and the Grand Theft Auto series still takes the world by storm.  Sony decidedly defeats Nintendo, but Nintendo does much better in this reality, since they keep most Japanese third party games and it is mostly just a 2-way race (after Sega leaves the market in the same way with the Dreamcast.)  Platform totals are something like Sony 140m, Nintendo 60m.

Generation 7 - Microsoft witnesses the domination of the PS2 and craps their pants.  They release their first console in this generation, but they do it a year after Sony and Nintendo, just trying to get their first console out there to learn the console business.  This generation is the first Nintendo home console designed with Iwata as CEO, so they still go the Wii route.  This alienates third party companies mostly the same way that the original Wii did.  PS3 also launches at the same stupid $500/$600 price and sells slowly at first.  This generation plays out mostly the same except Microsoft does somewhat worse and this benefits Sony but also Nintendo somewhat as well (since in our reality the 360 was trying to be the "family console" for a while too).  Nintendo narrowly wins.  Totals are something like Wii 115m, PS3 105m, XBox360 50m

Generation 8 and later continue to play out like our reality.  In the end Nintendo is Nintendo, Sony is Sony and Microsoft is Microsoft.  In spite of one key move changing things in the past, these companies still have patterns of behavior that they are going to fall into, and eventually things will end up like our reality again.