In this context, the license is for using the Arduino Studio application. This is hosted by Arduino, and therefore needs to take user input, save it and work with it. As I understand it, this puts them in a complex situation: they don't own the code you've written (obviously), but they do need to do things with it like compile it and run it (when you press the button in the IDE). They're also hosting the code and therefore partly legally responsible for it.

At the very least, you need some sort of user agreement to specify the things you can do with their content, otherwise you can't really do it because it's their content and you're not allowed to mess with it by default. (Like you said, code is copyrighted by default.) You also need to specify the things that are necessary by law because you are hosting that code and therefore in part responsible for it. You also don't want to make the user sign a new agreement every other week if you add some new feature that they need to agree to use, because the cost of all those legal documents is prohibitive, and it's also very bad UX.

Added to this the fact that lawyers are naturally very conservative as a profession (generally only doing things that have been proven successful, rather than avoiding things that have been proven unsuccessful), and it's easy to see why these sorts of agreements tend to be more expansive than they perhaps need to be, in order to ensure the company is fully protected.