Take a story's temperature by studying its tone. Is it hopeful? Cynical? Snarky? Playful?
It's hard to talk about tone in a play because it's all dialogue. There is no "narrator" who takes on a certain attitude toward the material that he writes about. It's always the characters speaking. Yet, because Stoppard's play works within the framework of another play, and because his characters sometimes act as if they know they are on stage, it does seem as if the playwright is a sort of presence on the stage. It's like he's a ghost floating around occasionally cracking jokes with the audience – "I know you're just watching my play and you know you're just watching my play and this knowledge allows us to make funny comments about the fact that we're really just playing 'make believe'." There are certain aspects of the play that are impossible – like all the Tragedians climbing out of one barrel, or Ros and Guil disappearing instead of dying, which again points to Stoppard's deft hand. It is, in short, very clever, and Stoppard takes a comic attitude toward his material, no matter how serious it sometimes seems to be (see "Genre" for more on his comic take).