No. You don't have to be a manager, but you do have to do more than sit in your office and code your little chunk of the universe because any kid out of college can do that. Heck, an awful lot of people out of high school can do that and don't necessarily require even a living wage.
Older programmers should be mentoring and leading. You don't have to have "manager" in your title to do that. The best programmers are the ones who can lead teams of more than 8 programmers, orchestrating the whole product life cycle. Generally, they contribute code too, but they also worry about repeatable testing, providing a release plan, code hygiene and standards, integration and customization points, and testing.
I've been on both sides of the fence, hiring and looking for work as a programmer. This has always been the reality. Your skill set should be commensurate with the years of experience you've had, which means that you should show a certain professional maturity. If you haven't advanced your skills beyond code monkey in 30 years, you've got a problem.