He then goes on to justify this statement with a few paragraphs, too.
Unfortunately I don't find the justification that compelling :-) The only management problem specific to non-developers he talks about is "if you're not a hacker, you can't tell who the good hackers are".
First, there is an element of recursion there (how to you hire the great hacker that knows who good hackers are since you can't tell who a good hacker is?)
Second there is nothing special about software development. The same is also true of all skilled professions (how do you know who the good designer is if you have no aesthetic skills, etc.)
If hiring people is the only problem there are many simple solutions that good managers already know about (e.g. specialised head hunters, consulting in-house experts, auditions, etc.)
Graham's article is a good read - but to my eyes it's about hiring great hackers to code, not hiring great hackers to manage. He even discusses mechanisms for isolating them from end-users to get them productive. Hardly a feature for a manager!
The other time he talks about management:
This is an area where managers can make a difference. Like a parent saying to a child, I bet you can't clean up your whole room in ten minutes, a good manager can sometimes redefine a problem as a more interesting one. Steve Jobs seems to be particularly good at this, in part simply by having high standards.
he's talking about Steve Jobs - a non-developer.
So I come back to the question - what exactly is your manager role's responsibilities, and why do you think that a non-developer won't be able to do them?
(I'm not trying to say that a developer would necessarily be bad for the role. Good managers with a techie background do exist. I'm just saying that, for a management role, I'd be more interested in good management skills rather than good software development skills. Better a good manager with no developer experience than an average manager with developer experience. Good managers can learn what the need to know.)