The bones of her argument are not semantic. She's saying that there is a sharp difference between consensual power and non-consensual power. The fact that she uses the word "power" to refer to the former and "violence" to refer to the latter is not that interesting. The distinction itself is what's interesting.

I agree with her that there's a distinction to be made between, on one hand, a group of people agreeing to follow a set of rules to accomplish some goal and, on the other, a slave driver forcing his slaves to accomplish that goal.

The idea that there is no real distinction here, that all power is based on coercion, was popular when she wrote the linked essay and it's popular today (as evidenced by the replies here). I used to think that way but I no longer do and, I have to say, it's quite a relief.