The article says this like it's a new problem. Automated resume screening is a long established practice at this point. That it'll be some LLM doing the screening instead of a keyword matcher doesn't change much. Although, it could be argued that an LLM would better approximate an actual human looking at the resume... including all the biases.
It's not like companies take responsibility for such automated systems today. I think they're used partly for liability cya anyway. The fewer actual employees that look at resumes, the fewer that can screw up and expose the company to a lawsuit. An algorithm can screw up too of course, but it's a lot harder to show intent, which can affect the damages awarded I think. Of course IANAL, so this could be entirely wrong. Interesting to think about though.