I did invoke feelings - the example was someone paralysed with grief and another person coming over to console them. Which of those do you think is the sociopath?

Managers shouldn't be making empathy conditional in the usual sense of the word, it is necessary in all settings to maintain an orderly, pleasant and respectful workplace. The article probably means something similar to but ultimately not exactly empathy. Probably sympathy, which gets used in the same paragraph. High empathy, low sympathy is par for the course for a good manager in a hard conversation.

One of the things I learned in Therapy is that other people’s emotions are their own. I can recognize them without living them myself and that’s okay. And I can be present for someone else by acknowledging how they feel without trying to change it. And it’s also okay to let other people know when you think they’re not seeing something that might change how they feel.