You've been able to purchase Wii U and 3DS games via the web for a while now.
But it's not built very well. And it only works for certain (Nintendo published, primarily) games. And you have to redeem the code in your email to get your system to background download it.
Basically, they half-assed it. The UX is bad all around. I'm really hoping they'll redo their entire online store.
It isn't out in the west yet but Nintendo Account in Japan is a lot better.
So you sign into your account on the nintendo Japan website, and you get a column to the right notifying you of any offers going on or new releases.
That aside, the Nintendo JP site becomes the web store, so you find the game you want (either through the front page marketing or maybe the 3DS software list) and then you click the eShop button, enter your card details, and the game starts downloading to your 3DS as soon as the transaction has finished.
I like this approach -- it allows for a more flexible shopping experience. For example, to download BOXBOY 2 onto my 3DS only took about 3 clicks to my card details:
Nintendo JP homepage -> Click BOXBOY 2 banner -> Click eShop button on the game's webpage
It'd be nice if third parties could integrate that eShop buy button onto their web pages for their games, so if you went on, say, the webpage for Yokai Watch 3, you could buy the game then and there on a whim.