Also shares same root as Engine I assume. Engineers are experts in system building or some kind, the earliest being weapons, then transportation, etc.
Software Engineer is 100% an engineering role IF you are making what could be called a kind of engine. Prime example is working on a game engine's source code, and design (i.e. Unreal, Unity...), or working on a custom operating system. I've seen many people try to downplay how much software has these "engine-like" properties, where you have to pay attention at the "moving parts" (runtime), and those people simply don't see the invisible machine that's doing the work.