I would prefer a more specific definition that would match more closely to people's intuition about what is and isn't a state, and also allows for discussion about what the state should and shouldn't do. If we define "state" as to include animals protecting their territory, I don't see how the term will be very useful in any discussion.
I think it's a specific rejection of the notion that there ever existed a time before governments. Governments existed, in some form, the moment particles started interacting.
I hadn't thought of it in those terms but I like that understanding of governments. A cell is a state, its laws are its DNA, and its borders are its membrane; and not just metaphorically speaking.
One useful reason to define states as such is because it's a definition that draws on the natural world. If states are only natural, and inevitable, then we don't have to argue about whether they are fundamentally good or bad.