I showed these photographs to several coworkers who lived all their lives in Vicksburg, and none knew anything about the site. It was too far from the old Ken Karyl School (now the Vicksburg Family Life Church) and across a busy street to have been associated with the school. If anyone has any information, please comment.
Update, March 23, 2013: I spoke to an old friend, a retired City of Vicksburg employee, about this site. He said it was still an official city playground but was not sure if the Parks and Recreation Department maintained the site any more. He recalled buying some of the playground equipment many years ago. He said the access road was once one of the National Military Park loops, but when the City and Federal Government exchanged land, part of Confederate Avenue was relocated and the city built the playground on the loop.
Photographs taken with a Panasonic G3 digital camera with Lumix 20mm f/1.7 lens. On this camera, I can set the aspect ratio to 1:1, which lets me frame square. I learned to appreciate the square viewpoint after using Rolleiflex twin-lens reflex cameras for 30 years. Raw files processed with Photo Ninja software on a Mac computer. I recommend Photo Ninja highly (but I recommend using film in a Rolleiflex even more highly).