Maybe there's a good argument for nonviolence but "the means dictate the ends" isn't it imo. It could be that there's more to it in the book but presented as is I'd say it doesn't follow logically, I'm going to want to see proof that it's actually true which is going to be tricky because there are obvious counter examples.
The easiest one is probably Ukraine. I'm sure most Ukrainians want to live in a peaceful and nonviolent society, but if they took your principle to heart there would be no Ukraine right now.