Nintendo hasn’t made a final decision about it though.
Recently, it was revealed that Nintendo eShop purchases would be tied to one’s Nintendo account. This was conveyed via the console’s initialization menus. Given how the previous system tied digital purchases to your console, leaving them to the mercy of machine life, this was good news indeed.
However, there seem to be some restrictions in place still. As per a Q&A session with Nintendo Entertainment planning & development general manager Shinya Takahashi (via YouTuber CrazyDopetastic) for a preview event of 1-2-Switch, someone in the audience inquired about whether games purchased games from the eShop once could be playable on two consoles should he buy one for his kids.
Speaking through a translator, Takahashi said that, “Currently we don’t have a system like that in place for Nintendo Switch. but we haven’t made any final decisions about how we would approach that going forward in the future, so unfortunately I can’t provide any concrete answer for you right now.”
By the sound of it, this could mean that games on your Nintendo Account sync to a single machine at a time. Granted, it could be a translation error but at the very least, it doesn’t sound like you can access your account across multiple machines at once.