The genre and associated genre expectations of "A Modest Proposal" differ depending on whose perspective one considers. The author and the narrator have different perspectives in the essay, so one must address the "author's genre" and the "narrator's genre" as separate but complementary devices.
From the perspective of the Proposer, "A Modest Proposal" is a persuasive, nonfiction essay that seriously suggests a solution to the suffering of impoverished Irish people. The Proposer's earnest tone evokes that of other 18th-century political essayists, whom Swift is undoubtedly satirizing. Taken from Swift's perspective, "A Modest Proposal" is a satirical essay that proposes a violent solution to the problem of poverty and colonial exploitation, calling to attention the inherent violence of the aforementioned.
Swift originally published "A Modest Proposal" anonymously, treating it as though it were a serious proposal being made by a well-intentioned intellectual as opposed to his own satirical take on the subject matter. At the time of its publication, many readers responded to the essay's content with disgust and outrage, reacting to the anonymous writer's proposal in earnest. During this period, many anonymously published political pamphlets were written seriously. Given that the genre expectations of Swift's audience aligned with that of a persuasive and not a satirical essay, it is unsurprising that many took "A Modest Proposal" at face value.