With that logic, Sony went third party too with their mobile initiatives. Hell, MS is already half-way there with publishing Minecraft on literally everything.
As for the second point, the Switch is for all intents and purposes a platform that competes with what MS and Sony has. Trying to define it as anything but is silly and is largely an argument of semantics.
Sure, if Sony are making games for iOS and Android then they absolutely are a 3rd party dev in that regard. For Nintendo, though, it was seen as this big deal that they'd never have their in house developers design games for software they hadn't designed themselves. There was this argument that the synergy between their hardware and software was too precious for them to lose, that without said synergy that the games wouldn't be "Nintendo games".
All 'going 3rd party' ever meant was breaking that philosophy and developing for other people's hardware. It never meant that they would stop developing their own hardware, and I certainly never argued as such. So the fact that they are developing for mobile was them going 3rd party, and it was a really momentous decision. A big deal.
And as for the Switch, it's not semantics, because the fact that Switch is a portable console is a large part of what is making it so attractive to consumers. If the Switch was, in fact, a dedicated home console would it have anywhere near the success as it has? I don't think so. Me personally, I use it as a home console 95% of the time. But that doesn't change that the systems unique selling point is its hybrid nature - that it is a portable that can hook up to your TV.
Again, it's not semantics when the portable nature of the device is intrinsic to its success, with sales more in line with previous Nintendo portables than home consoles. I don't see why Nintendo would try another dedicated home console given all of this.
Switch is a dedicated home console. I can play it on my TV, is a home console regardless of mental gymnastics. "Going third party" meant stopping creating hardware, which they did not.
You tried iT, shady and cheerful animated cloud.
Answered above. I always argued that they should continue making handhelds and start making mobile games. I called that 'going 3rd party'. That's what they did. Maybe that's not what others meant, but it's what I always argued.