That being said i do think you could have made your point more succinctly.
For a while, it seemed like you were arguing semantics vs actually informing the reader.
Your point is valid. I'm not sure how to present it better, but I'd posit:
"Sparta, the city, was not 80% slaves. That stat only true about the state. This distinction only matters because the author is critizing sparta society on the basis that Sparta's seat of power was slave-cornucopia. But this is false. Sparta the city is mostly spartan citizens, making the author's criticism-by-sleight-of-hand dishonest"