This will be a dramatic reversal of the last cycle during the mid-to-late 2000s, when the Nintendo Wii left its competitors in the dust (the PlayStation 3 and Xbox 360). In fact, it will be a return to Nintendo's status from roughly the mid-'90s through the early 2000s, when the Nintendo 64 and GameCube were passed over for the new consoles by Sony and then Microsoft (PlayStation and PlayStation 2, and the Xbox).
Before the reign of the Wii, the previous heyday of Nintendo was the '80s and early '90s with the original NES and the Super Nintendo. In the early and mid-'80s, they had also released a string of popular arcade games: the Donkey Kong games (which were also ported to home consoles), Mario Bros., and Punch-Out.
Already by the early-to-mid-'90s, the Sega Genesis looked poised to dethrone Nintendo, although the coup de grace would not be struck until the release of the PlayStation in the mid-'90s.
Putting it all together, Nintendo has been popular during more sociable times (the '80s, the early '90s, and the blip of the mid-late 2000s), and fallen by the wayside during more cocooning times (the mid-'90s through today, except for the recent blip).
What accounts for this? Beats me, but Nintendo does have a consistent approach of making video games for everybody and giving them an easy-going and lighthearted tone. We don't have to stretch the imagination to see how such games would be more popular when folks are more outgoing and fun-loving.
Their competitors have also employed a consistent approach in the opposite direction -- edgy, in-your-face, too cool for your parents, ultra-violent, hardcore gamers only, and so on. Basically, for the bitter dork who locks himself in his room to take out his rejection-anger on video game characters (at first those controlled by the computer itself, and later those controlled by other people, with the ability to play online). Again, no stretch to see how this mode would appeal to kids when young people are increasingly withdrawing from social interaction.
Some trends in video games over the outgoing and cocooning phases of the social cycle may require you to look at things on a fine-grained level, but here we can see a suggestive pattern at a bird's-eye-view.