Nintendo has videos about removing Switch emulation from Steam Deck – Gaming

This is a selective quote. The second sentence is complete again:

Use of unauthorized system or software, which permits technical modification of the Switch hardware or software, may render this software unusable.

It is not about using the game on other devices, but about using or misusing this software to make technical modifications to the Switch itself or the games. So basically he’s abusing the loopholes. If you do, you expose yourself to consequences such as a ban.

This is quite different from making a backup of your game (although of course this is subject to other legislation), where you are not tuning the game itself and also not tuning the same switch (although this may again be subject to other legislation), See the Gary Bowser case).

So no, their terms do not state that you cannot use the software on other devices. Only if you use their games in an inappropriate manner, they reserve the right to restrict the use of the game or any additional services. Fair enough, but this makes playing the game through an emulator neither illegal nor against its terms.

Edit: By the way, I totally understand your approach in this regard, going back to your first comment Naturally, the emulation principle itself is completely legal and shows which programs have been emulated as well. But the means to get here are already in a deep gray area (in many countries anyway), not to mention the public’s intentions. But the way Nintendo is trying to bury things is also a very gray area in my opinion. In fact, a copyright claim is made to take something offline that may or may not have an illegal basis. They cannot prove the latter, so stop such force majeure.