I think the latter is what OP referenced, if someone is telling you "it's my way or the highway" and they are OK with the highway option, you should listen. They are telling you exactly how much you are valued (or not), as well communicating that they feel they are in no uncertain terms above you.
As you say, an ultimatum isn't necessarily abusive. We all have things we want in life - and some of them are deal-breakers for a relationship. But if you read the sentence as written, I think it's solid advice - don't agree to something when someone is leveraging "power" over you if you can avoid it. That is abusive.
People who've been in abusive relationships can read the difference between a "this is make-or-break for the life I want, you need to make a choice" and "I'm abusing this situation to make you agree to something you don't want to do / is bad for you."
The latter is an ultimatum, there's no way around that. Whether or not the ultimatum is reasonable depends entirely on the specifics, especially in the workplace, employers have expectations which they need to have met.
It's especially distasteful to bake in the assumption that a romantic partner setting conditions to stay in a relationship is automatically being abusive. If someone is presented with an ultimatum to quit problem drinking or lose their partner, which is more likely: that the partner is abusive or that the other partner is an alcoholic? It's certainly not automatic that it's the former!
A policy of never meeting an ultimatum is one way to live your life, I prefer to consider whether the demands are reasonable and proceed on that basis. For me it shows a stronger sense of self worth to consider this kind of thing on the merits, rather than pre-committing to stick to my guns, which is in effect a counter-ultimatum. Sometimes that's the right move, sometimes it isn't.