> People management was always only a branch of management.

What other branch is there? You are either delegating or doing all the work yourself. Those who delegate become seen as managers, as that delegation requires managing the people (or, possibly things, depending on how you see that) that the work was delegated to. Those who receive the delegation and carry out their task individually are those considered to not be managers, but rather individual contributors.

> However, never would I say that when coding, I'm "managing the computer".

Why would you say anything while coding? I guess if you had some kind of voice-to-text system you might say something, but it wouldn't be "whee, I'm a manager now!!!!" — it'd be specific instructions directed at the computer so that it knows what task you are delegating to it.

> A compiler is a tool, not an unpredictable process I need to manage.

A compiler can be predictable if you perfectly describe the task you want it to carry out. However, that rarely happens in practice. Communicating your intent is always the hard part.

Which isn't much different than people. There are exceptions, but generally if you clearly define what you want them to do, they will execute it perfectly. Management of humans is all about coming back to make sure that what you described was correct and made sense to the receiving party. Which is the same thing you have to do with compilers.