The right answer is alternative two.
In the passage which describes "Rosencratz And Guildenstern Are Dead," the author makes clear that Tom Stoppard is a playwright. Actually, he is the composer of such written work. There is no evidence that Tom Stoppard dislikes Shakespeare. In fact, he must admire him, since his play develops two minor characters from Hamlet. The excerpt does not mention any references to Stoppard's search for fame or that he reads many books either.