I find that one of Nintendo's key objectives in their business is to reach a wide audience, and I think that the phenomena that struck with Wii Sports where people ranging from children to elders were playing together is very significant to consider. For a long time since its release there would always pop up a news story on how like elders would have increased motor capabilities after playing Wii games, fitness instructors were using it in like gyms, and how like surgeons had increased precision after playing on the Wii (I have no source to back this up but it's likely you can recognize hearing some of these anyway) - not to mention the plethora of broken televisions that emerged from that era. I feel like they were able to reach such a wide audience in the first place because at the time, motion controls were revolutionary and a wider audience could understand how it works, just like how at the time, the NES was revolutionary because you could go home and play video games for the first time without hitting up an arcade. Of course, the big mark that the NES did was save the video game industry from the video game crash and it did indeed make Nintendo somewhat of a household name, but I think that although the Wii didn't quite save a falling video game industry, Nintendo being a household name was also supported by the Wii's release. Believe what you want, but I think the Wii was just as pivotal in Nintendo's mark in history as was the NES; it's debatable which one had more of an effect but I find it hard to say that the Wii was not a large effect.
Also, you can't say the NES is the very reason that Microsoft and Sony have video game consoles these days when you yourself stated that there are a "few other important consoles that [you're] forgetting"; you can say it is ONE of the reasons. The Intellivision, the Atari 2600/5200, and the Odyssey are prime examples that also were revolutionary in that they made a way for people to play, like, pong at home, and these came out a couple years earlier. Now, I'm not saying I don't like the NES in any way (and I'm not saying the Wii is without major faults as opposed to the NES - the Wii was officially acknowledged by Nintendo to have great limitations hardware wise and software wise, it did not give Nintendo the numbers they truly desired, and maybe the concept of reaching a wide audience did not appeal to everyone), I just feel that by neglecting the impact of other consoles your argument feels a bit more one-note/conceded, which isn't to offend you or your opinion, I just believe you're not giving these other consoles enough credit.