This is really weird, I didn't check it when I bumped the thread, but there is no eShop website per se; only the game pages in Nintendo's website has been updated with eShop links which shows price and rewards and those can be purchased with your NNID.
You can check the confusion in Nintendo Life's comments:
http://www.nintendolife.com/news/2016/03/nintendos_official_website_eshop_purchases_are_up_and_running
It's weird they did not make a proper eShop site dedicated to it, with nice filters and the latest titles and promotions... just like their nice My Nintendo site. Still it is fine we can do this in Europe, and have the change to buy stuff from a browser. Not sure if the US already had this option?