Defining fascism is famously described as like trying to nail jelly to a wall. You have given just one source of a definition of fascism.
Let's remember that both the movements of Mussolini and Hitler had their roots in socialism, they weren't called the National Socialists for nothing.
Specifically we can look at:
Totalitarian Control:Fascism emphasizes the subordination of individual interests to the state, similar to state-socialist models where the government controls the economy.
Economic Interventionism: Fascist regimes often rejected pure free-market capitalism, favouring heavy state intervention to direct economic production for national goals.
Populist Tactics: Early fascist movements sometimes used left-wing, anti-capitalist, and populist rhetoric to mobilize working-class, labor-oriented, and populist support.
Anti-Liberalism: Like some radical left movements, fascism strongly despised liberal democracy, individual rights, and pluralism.
State control of all education and healthcare is both a left wing and fascist ideology.