So the "lateral" thinking, here, was actually... quality. Smartphone games suck. The monetization strategies are downright predatory and touchscreens are a bad input device for a majority of game genres.
So what Nintendo did was make actually great games for a tablet device. Being able to put it on the TV and detaching the controllers is secondary, it's mostly about having great games!
This is why I'm a little pissed at marketing analysts turning this into some kind of stroke of business genius. The Switch is basically a Wii U with the GPU moved into the tablet part and the Wii U flopped hard. No market analysis could have predicted the Switch's success. It was a stubborn believe in quality, the worst thing they could do, what every "business advisor" would have warned them against. Market analysts were hilariously wrong and that's the history lesson to learn here, not "predulating quadrilateral core-market flibbugasting". The Switch is not a win they can claim, it's a win for quality and idealism.