I don’t believe they argued that the 13th amendment says prisoners are slaves. They only asked you to imagine that you are and they pointed out that it’s allowed “according to the Thirteenth amendment”. At least, that was my interpretation.
My read is that they were asking the reader to imagine they (the reader) are a prisoner, and thus a slave according to the thirteenth amendment. Even under your reading, that comment is a pure hypothetical, because federal prisoners are not slaves. I happen to believe that the federal government has enslaved people in a different context, very recently, conscripts.
They call it "involuntary servitude." I read it as:
Neither (slavery) nor (involuntary servitude, except as a punishment for crime whereof the party shall have been duly convicted), shall exist within the United States ...
