I own a Nintendo 2DS, which also included Mario Kart in the bundle. This console is now defective. I could now get a cheap new bundle with New Super Mario Bros 2. Can I somehow use the Mariokart with the new Nintendo 2DS, or how can I get the Mariokart from the broken to the new 2DS? In my imagination I would have the new 2DS with Mariokart AND Super Mario Bros 2, is that possible?
If you created an account for the Nintendo eShop on the defective 2DS, the pre-installed game was bound to it.
In this case, it is with the help of Nintendo Support even with a total loss to transfer the games from your account to your new 2DS / 3DS, there you can solve your NNID of the defective device.
According to what I found on the internet, you would have to write the email from the email address used to register the account:
https://bisaboard.bisafans.de/index.php?thread/295645-nintendo-network-id-vom-kaputten-ds-%C3%BCbertragen-lassen/
When you log in to the new device, the game that is preloaded there's bound to your account and you have both games.