In non-tech big companies at least, you don't need any clear skill set to be a manager. The really bad ones have zero skills whatsoever. A plumber has to know to fix a sink, a dev, write the codez. You'll be found out likely before too long if you manage to get hired and then have no idea (it does happen).
Many managers of technical people are not technologists, they're professional managers, and have no clear skill sets. There's not one useful thing they can do incredibly well that not everyone could handle. (This the ONLY reason you can make $100k in the US by just writing code, by the way, many people can't handle, nor want to handle, programming in C++).
They do have "Managerial Experience", and that gets them hired, even if they suck.. bad.. Even over the incredible technologist.
In their defense however, I would say the very good non-technical technical managers I've worked with, they know nothing about tech, but are so smart and savvy that you could throw complex stuff at them and they know exactly what you're talking about. They protect their people from political bullshit, defend them to outsiders when needed, sometimes hear out the occasional programmer temper tantrum, and schedule the work. That's where they add value.