User Experience design is Product Design. Any product with some level of complexity which requires a human to "use" it, requires User Experience design. Complexity can be defined by the number of user goals the product supports.
Something like a toaster, which has a single user goal (toast bread) doesn't really require user experience design.
Something like a website, mobile application or software application (all of these are products) has significant complexity and often supports many different user goals. Hence why in the digital domain, User Experience design has become so important.
In digital, like any domain, User Experience designers also need specific domain knowledge in order to design a good experience. So if you're going to be a UX designer designing digital products, you need to understand different user interface paradigms. You need to appreciate what technology can do and what it can support. You need to be able to create digital prototypes and be able to test them.
I spent the majority of my career as a UX designer for digital products (which included apps, websites, kiosks, terminals, public displays, interactive exhibits, etc.).
But I now work as a UX designer for Ford Motor Company. I still follow the same User Centred Design process, however the domain is now different, and with that comes the need to understand a lot of automotive-centric product concepts. Most of my prototyping now is done with polystyrene, 3D printers and cardboard!
Hope this helps!