Take a story's temperature by studying its tone. Is it hopeful? Cynical? Snarky? Playful?
It definitely seems like the play has a point of view that it wants to get across, which is why we label it a polemic. The Doctor fights to expose the truth of the Baths and the whole of society. We're willing to go out on a limb and say that not too many readers or audience members are rooting for the Mayor to silence his idealistic brother. When the Doctor goes off on his tirade about the dangers of rule by an ignorant majority, the true message of the play is revealed. This play is basically a direct assault on the foundation of democracy and is just as edgy today as it was when it first hit the stage.