It's not really just simple up-scaling where you'd take a 720p source image and just blow it up to be three times as large so that it neatly fits onto a 4K screen, but rather creating both 720p and 4K renders of the gameplay and training a neural network to take the 720p render as input and produce the 4K render as output. Obviously it can't get it perfect, but it just needs to be good enough that humans will have difficulty telling the difference while the game is running. The training for this is done by developers ahead of time so that it can produce a trained network that is run by special hardware on the console in order to handle the creation of the 4K image. The game ships with the trained neural network which is run on the specialized hardware when the console is plugged in to a TV and needs to output at 4K instead of to it's built-in 720p display.

Obviously it's not magic, but it's actually a reasonably solution for a piece of hardware like the Nintendo Switch which can't possibly include hardware to generate a native 4K image due to design constraints and the limitations of current computational power.