Nintendo gift cards can be redeemed via the Nintendo eShop or online at Nintendo.com. Once you redeem a Nintendo gift card, the balance can be used to purchase downloadable content such as games, features, movies and more. The game (or other content purchased) will automatically be downloaded to the system associated with your Nintendo account.
There is no such thing as a device-specific gift card such as a Nintendo Switch gift card or a Nintendo DS gift card. The all-encompassing Nintendo eShop gift card can be used to purchase content for any Nintendo-branded device—Nintendo Switch, Wii U or Nintendo 3DS – but you do need a Nintendo Account to complete the purchase.
If you redeem the gift card online at Nintendo.com, the content will still only be downloaded to the device associated with the account.
By the way, the character shown on the gift card does not indicate that the gift card must be used on a specific game. The Mario gift card, for example, is still a Nintendo eShop gift card that can be used to purchase anything available on Nintendo.