Yes, a manager is more like the coach of a sport team. Not really a part of the team proper as such. They can't be and still be able to do a huge part of their job -- acting as the interface between the team and the other parts of the organization.
A manager's job is to coordinate effort on a high level, to ensure that the team has everything it needs to function well, and to remove as many roadblocks as possible.
A managers's job is to "grease the skids" and run interference.
Never played at all would be strange (it seems uncommon to watch a sport you have never played, let alone make a career of it). It's pretty common in the NFL to see coaches who were never professional players and possibly only played at a small college to boot.
While one who has at least dabbled in coding is preferable, a great manager can be effective even if they've never written a line of code in their life.
I'd much prefer a manager who knows how to manage but not how to code over a manager who knows how to code but not how to manage.
That's obviously ideal. I didn't mention it not because it doesn't exist, but because I was trying to do a "compare and contrast" with the other two, more extreme, cases.
A manager's job is to coordinate effort on a high level, to ensure that the team has everything it needs to function well, and to remove as many roadblocks as possible.
A managers's job is to "grease the skids" and run interference.