Anxiety
The story follows Tchervyakov as he commits an accidental faux pas (sneezing on someone, and in this case someone of a higher rank) and proceeds to anguish over his mistake until it eventually causes him so much strife that he dies. Both Brizzhalov and the reader know that Tchervyakov's offense was unintentional and minor, but in Tchervyakov's mind, it was cataclysmic. The story presents Tchervyakov's anxiety over the incident as completely unwarranted (compounded by Brizzhalov's pleas to dismiss the occurrence altogether), but nonetheless all-consuming. Thus, Tchervyakov's becomes a casualty of his own anxious thoughts, spurred by his exaggerated concern for social mores.
Class and Power
Of course, the stimulus behind Tchervyakov's crippling anxiety is the fact that he sneezed on Brizzhalov in particular – a higher-ranking government official with the power to destroy Tchervyakov's career and livelihood. While the story makes a joke of Tchervaykov's over-the-top shame for his sneeze, it also in some ways validates Tchervyakov's behavior, especially when his wife seems to share the same worries. Tchervyakov's anxiety is therefore indicative of a larger problem in the story – the extreme disparities between social classes – and it is this strict social hierarchy that becomes the real target of Chekhov's criticism.
Absurdity
Ultimately, the premise of the story is an absurd one: that something as insignificant as a sneeze could eventually lead to a man's death. The hyperbolic nature of the narrative helps emphasize, however, the problems with the more realistic aspects of the story, such as the need for lower classes to behave with utmost decorum around wealthier or higher-ranking members of society. The absurdism of the plot ultimately helps reveal the absurdism of arbitrary rules society continues to uphold.