Populism is a "thin" political ideology that often gets layered on top of other political ideologies, both left- and right-wing. It simply means "policies that appeal to ordinary people" (vs. a rich and perceived corrupt elite). By definition, someone who hates billionaires simply because they are billionaires is a populist. They might hate other populists that have attached themselves to other political ideologies (and have different scapegoats or preferred policy prescriptions to rectify the inequality), but they are still a populist.

> By definition, someone who hates billionaires simply because they are billionaires is a populist.

You've ascribed to them an ideology they don't hold. They don't hold that view "simply because they are billionaires".