They were technically horizontally integrated too, since the entire reason they were able to exist is situations where jobs like mining were created in isolated

They were technically horizontally integrated too, since the entire reason they were able to exist is situations where jobs like mining were created in isolated areas with no other places to live. Workers had no other options but to live in that company town and spend their money in company town stores. All vertical integration means is that a company has direct control over most/all of the supply chain they need to get their product made and sold. They don't need 3rd parties to supply them with any of the steps in the process. That obviously gives them a competitive advantage, but it doesn't involve directly removing other competitors the way horizontal integration does.