From the linked article itself, I can attest to the constant push to move up into 'leadership' roles, particularly in some companies. I have stayed and worked as an engineer for 37 years. I have been 'team lead' a half dozen times, but never a full manager role. Why? Because I would be a poor manager. I have personally experienced managers that where technically brilliant, but not good at managing (or inspiring) the technical staff. They should have remained as engineers/scientists. Some corporations used to have parallel paths for technical staff that had management level pay and benefits, but the suits in the 'C suite' have eliminated that for the most part over the last twenty years. Bell Laboratories (now a shell of its former self) was once one of those places.
So in the current environment, there is constant pressure to move up or move out. Even startups are no longer immune to that. If you want to have enough shares for it to really matter in a liquidity event, you need to have a team of people below you, or at least a director level title. The startup environment in 2000 was completely different, and technically astute engineers (mechanical, electrical, software) could attract strong stock grants as engineers. That has changed. I am fortunate in that after 37 years of doing this, I am at a position where I don't even have to think about these issues any longer. I feel sorry for younger engineers breaking into the field, the management pyramid is such a PITA.
And back to the topic of strong technical engineers that are poor managers? If you get stuck into one of those situations, constant micro management, constant downward pressure of "you don't know what you are doing", get out. Find a new position elsewhere. Good managers will coach you when you need help, but will let you do your own work. Good managers will help identify your deficiencies but also guide you to work that plays to your strengths. Good managers will provide you opportunity for growth. I learned this early in my career, blessed with having an awesome manager. Since then, every job I have had, first thing I did was figure out which managers were good, and which ones were not, and made sure that I never had to work under a bad manager.
So you can make a career in engineering, but it has to be a choice, and you have to learn to manage your managers.
Also note, while I recognize that I would be a poor manager (for various reasons), mentoring is a different skill set. If you are a senior engineer, take every opportunity to mentor a starter in the field.