The body in the story isn't so much a symbol or an allegory as something emphasized in the story. The punishment of a condemned man has a lot to do with his body. Not just because it's an immensely long, painful, and elaborate way of torturing the body, but because the condemned man learns his sentence through his body, "through his wounds," as the officer says. It's as if learning through the body is deeper, somehow, than learning through the mind, so that torturing the body has a definite meaning. The control the penal colony exercises is over the body, whether it be through the prisoner's chains or the devilish workings of the apparatus.
The story is also chock-full of nasty images of the body. There's the condemned man's ugly, doglike face and the officer's "uncommonly limp" face that "breathes with the mouth wide open." Then there's all the icky bodily oozing we see in the story: constant sweating from the explorer and especially the officer, who's roasting in his uniform, the condemned man's vomiting, and all of the blood generated by the apparatus. And there's that lasting, gruesome final image of the officer with the spike through his head. Throughout the story, then, we're constantly called back to the body, in rather revolting ways.