I doubt that what he does in that position is purely managerial. I think you may have a hard time seeing why they value what they do if you impose your own viewpoints on them.
In my opinion, it will be impossible to have 200 employees with a flat structure.
I think the misconception with the article is that the title (and focus) is "Why I run a Flat Company" as if this should be the standard for modern business. This works for 37signals, because (1) you have actively chosen to grow very slowly when you could have otherwise grown much faster and (2) you've had the fortune and ability to attract some very good people. Many businesses don't desire to do number 1 and find it very hard to do number 2.