There are engineers convinced that they are smarter than everyone else but that isn't what is happening in this vignette at all. Even with my grave concerns about how accurate the reporting is of what he said, half the story is the reportee trying to figure out what he's done wrong and how to stop his manager from beating him with a rhetorical stick. That isn't the action of a man convinced he is the smartest guy in the room. But it is the reporting of a manger who believes beating someone else with a rhetorical stick makes him look good.
I'm not even saying this guy is a bad leader overall; at least he isn't being especially passive aggressive and this doesn't say anything about him at his day-to-day. But if he understood what attitudes and behaviours he was displaying in this story he wouldn't have been so keen to publish it. People who've had to deal with abusive people in power positions are going to have alarm bells going off reading this. It looks like someone lying to themselves and the reader in order to feel good about wielding power. Although, reading charitably, it might just be ignorance and low-grade communication ability.