Solution: In System Settings, I changed the Video Render scratch disk to another drive, and subsequently the proper Render Manager window appeared. Then I went back to System Settings and switched to the previously selected Video Render scratch disk. The Render Manager window continued to read as it should.
I guess a glitch in FCP can cause the Render Manager window to format as the Browser window. This doesn't seem to be specific to FCP6, as I found a reference to the same problem mentioned in LAFCPUG dating back to 2003.