My specific goal with this was to understand the mainstream anarchist/ancom definition of a central point of anarchist thought.

I would very much disagree that definitions are not important (but would differentiate between clear definition and semantic arguing).

Like in Marxism how people define socialism can be a categorically opposed group of people.
Without definitions, words have no meaning and theory becomes useless. And without revolutionary theory there cannot lasting revolutionary praxis!

TL;DR: We should be clear about our goals and our enemies. Since I wanted to genuinely understand a crucial part of anarchist thought, I very much am interested in definitions.

Edit: Political economy is a science (even if a "soft"/social one) and the scientific method of analysis requires clear terms.

Of course we are also talking about Philosophy here, but even there, useful discussion cannot be had without consensus of basic definitions.