This depends on what you think a manager's job is. If you think it is to "be the boss", to run things, to make decisions, to tell people what to do, then yes, relevant experience matters.

But there's another view of a manager's job, and that is to create an environment where they can get their work done without having to worry about bullshit like schedules, budgets, and politics. For that kind of a role, a non-technical person can be a great fit, possibly better than a technical one.