To answer the question in the title: by citing old court decisions in cases that involved slaves. For example (the article gives zero examples, so this is hypothetical), if someone promised to deliver a slave, failed to do so, and was then found in breach of contract, this could be cited as precedent that a verbal promise can establish a business contract (notably, it cannot be cited as precedent that people are property, due to the 13th amendment). By the article's unstated logic, this is "continuing to treat people as property".