During the Switch Presentation Nintendo announced they will be offer paid online services that includes a “monthly game download”, but it appears like there is a major catch with this.
Nintendo’s site says..
Monthly game download
Subscribers will get to download and play a Nintendo Entertainment System™ (NES) or Super Nintendo Entertainment System™ (Super NES) game (with newly-added online play) for free for a month.
Despite this claim, Chris Kohler of Wired says that these games will only be available for free during the month it becomes part of the deal and unlike Xbox Live Gold and Playstation Plus, you will not be able to play the game once the month ends. You will have to purchase the game in order to play it again or hope it comes back as the free game of the month.