populism as an ideology that presents "the people" as a morally good force and contrasts them against "the elite", who are portrayed as corrupt and self-serving ... Populists typically present "the elite" as comprising the political, economic, cultural, and media establishment, depicted as a homogeneous entity and accused of placing their own interests, and often the interests of other groups—such as large corporations, foreign countries, or immigrants—above the interests of "the people".
It's generally defined by a claim to represent some unified idea of the "true people" as opposed to the corrupt elites running everything.
Stewart is not pretending to represent anyone, he's just a guy highlighting problems and making jokes on television. If he ran for office he could decide to use populist or non-populust rhetoric.