It only changes the kind of management responsibilities you're talking about. Yes, some positions will have zero employee management, however you'll be responsible for product management. There is no product in a big company that can be created with zero collaboration, so you'll be responsible for managing collaboration with other groups, determining features and getting ok from management, making sure that others are doing their work, etc. It is management nonetheless, sometimes with lots of meetings, just with a different goal.

Most companies are not "good" engineering companies. They are at best mediocre.