Software or hardware engineering is a solution. You can solve the same with a pen and paper if you know what the user needs.
Agile is a way to iteratively validate expectations and revisit and update things with minimal wastage
Perhaps you're using the word "engineering" as a synonym of "implementation" (which could work); I'd have thought it was more "design" though (in a technical sense, though I'm sure it might cover some of the aesthetic sense too).
Negotiation of requirements is a problem based on limitations like recources (money, people), known knows and known unknowns.
Good engineering requires making the correct decisions in those cases. It requires knowing the 'actual' problem so you are not building a solution for the wrong thing. That means requirements are a part of engineering. Maybe not the full responsibility of gathering requirements, but understanding requirements, clarifying requirements, and feeding back what requirements are feasible or conflicting seem very much a part of engineering.