The current gen version actually came out yesterday, I've bought it already despite having it for 360 and PC (XB1 version, mainly for the missus)
Skyrim was an odd choice for show anyway if you ask me - why take [the HD version of] a 5 year old game, that frankly plays very similar to the new Zelda game you've just piggin' shown a few seconds earlier, as if it means as much to your fans as that game does?? I'm a massive Elder Scrolls fan, but having an old-ish entry almost overshadow your flagship Zelda was round the bend if you ask me.....
Suppose it's big news if only to show that Bethesda are on board - perhaps Fallout 4 would've been a better choice title though..?
In my opinion Bethesda, CD Project and Rockstar have the best company philosophy in the gaming industry. They rely on quality instead of mass production like Ubisoft, EA and so on. Skyrim is one of these few evergreens and it's impressive that they're (hopefully) able to port this jewel onto a "handheld". I think the message of Nintendo is not just: "Hey, we've 3rd party support" (then they could show FIFA17 or stuff like that) but also "Switch has the power to manage this huge game." Yes, for a pure home console this would be nothing special but for a handheld it's impressive. With a brand new 3rd party game they would not be able to transport this message in that way. I had also preferred to see Witcher 3 or GTAV in the trailer ...but they've chosen Bethesda and if they currently have no Elder Scrolls 6 in their backhand because they're focusing on Skyrim SE ...they've shown Skyrim SE.
And about the comparison of Zelda and Skyrim: For me Skyrim looks way more next gen than Zelda even if it's 5 years old. It also has the deeper gameplay, the bigger map and dungeons (just guessing) and it is completely synchronized. Yes, Zelda is another genre and has an own style but (for me) it's not impressive - Neither in the trailer, nor for a "Next Gen console" in general.
People are also buying their favorite movies on VHS, DVD, BluRay because they can enjoy it in another way again and again. Skyrim is such a classic/milestone and the fans will buy this game + NS to experience it in a new way (on the go). It was a good choice by Nintendo and Bethesda.