In 1984, Orwell describes the imperialism using the fictional book The Theory and Practice of Oligarchical Collectivism by Emmanuel Goldstein, which is clearly inspired by Marx's doctrine. But he never uses the world "class", saying instead that "there have been three kinds of people in the world, the High, the Middle and the Low." Why?

While Orwell's (Goldstein's) book is inspired by Marxist theory, Orwell tries to accentuate the differences between Oligarchic Collectivism and Marxism. Both Marx and Goldstein have a theory of history, but they veer away from each other in significant ways. Marx saw an inevitable end of history in which the working classes rose up, killed the capitalists (he saw no alternative to violent revolution), took over the means of production, and distributed profits equally among the people to create, ultimately, a stateless utopia. Goldstein, on the other hand, theorizes a quite different outcome: the "High" will consolidate and perfect their power and use it to stay in control forever, increasingly crushing and dehumanizing the Middle and Low.
Using Marxist class markers such as "working class" and "upper class" would not only have the potential to confuse this theory of history with Marxism, it would overcomplicate what Orwell/Goldstein is trying to say. A larger context for the quote follows:

. . . there have been three kinds of people in the world, the High, the Middle, and the Low. They have been subdivided in many ways, they have borne countless different names, and their relative numbers, as well as their attitude towards one another, have varied from age to age: but the essential structure of society has never altered. Even after enormous upheavals and seemingly irrevocable changes, the same pattern has always reasserted itself, just as a gyroscope will always return to equilibrium.

Marx talks about how society changes as the basic ways of creating wealth changes: hunter/gather societies differ from Medieval land-based societies, which differ from modern industrial societies. Orwell/Goldstein simply isn't interested in all this: the concern here is simply with the mechanism of power.