Can world systems theory apply to empires?

It can.

Countries are decidedly not the primary unit of analysis, nor are regions. It's got its name because it looks at the world and how the emerging structures create and recreate unequal relationships. Boundaries are fluid and of low importance. Whether for a state, a region, or an empire.

That we see it often attached to entire countries now is probably because of the theory's usefulness for analysing development processes and globalisation issues.

As such, the frame of reference can be less macro, and focus for example on cities and their place and function within the system. The Core-periphery-structure 'scales' well.

As Wallerstein's model is said to be

aiming to replace modernization theory, which Wallerstein criticised for three reasons:

• its focus on the nation state as the only unit of analysis
• its assumption that there is only a single path of evolutionary development for all countries
• its disregard of transnational structures that constrain local and national development.

Wallerstein offers several definitions of a world-system, defining it in 1974 briefly:

a system is defined as a unit with a single division of labor and multiple cultural systems.

He also offered a longer definition:

…a social system, one that has boundaries, structures, member groups, rules of legitimation, and coherence. Its life is made up of the conflicting forces which hold it together by tension and tear it apart as each group seeks eternally to remold it to its advantage. It has the characteristics of an organism, in that it has a life-span over which its characteristics change in some respects and remain stable in others. One can define its structures as being at different times strong or weak in terms of the internal logic of its functioning.

In 1987, Wallerstein again defined it:

… not the system of the world, but a system that is a world and which can be, most often has been, located in an area less than the entire globe. World-systems analysis argues that the units of social reality within which we operate, whose rules constrain us, are for the most part such world-systems (other than the now extinct, small minisystems that once existed on the earth). World-systems analysis argues that there have been thus far only two varieties of world-systems: world-economies and world empires. A world-empire (examples, the Roman Empire, Han China) are large bureaucratic structures with a single political center and an axial division of labor, but multiple cultures. A world-economy is a large axial division of labor with multiple political centers and multiple cultures. In English, the hyphen is essential to indicate these concepts. "World system" without a hyphen suggests that there has been only one world-system in the history of the world.

Since Wikipedia falls short on quoting context:

Note the hyphen in world-system and its two subcategories, world-economies and world-empires. Putting in the hyphen was intended to underline that we are talking not about systems, economies, empires of the (whole) world, but about systems, economies, empires that are a world (but quite possibly, and indeed usually, not encompassing the entire globe). This is a key initial concept to grasp.

It says that in “world-systems” we are dealing with a spatial/temporal zone which cuts across many political and cultural units, one that represents an integrated zone of activity and institutions which obey certain systemic rules.

Actually, of course, the concept was initially applied primarily to the “modern world-system” which, it is argued, takes the form of a “world-economy.”

This concept adapted Braudel’s usage in his book on the Medi­terranean, and combined it with the core-periphery analysis of ECLA. The case was made that the modern world-economy was a capitalist world-economy – not the first world-economy ever but the first world-economy to survive as such for a long period and thrive, and it did this precisely by becoming fully capitalist. If the zone that was capitalist was not thought to be a state but rather a world-economy, then Dobbs so-called internal expla­nation of the transition from feudalism to capitalism made little sense, since it implied that the transition occurred multiple times, state by state, within the same world-system.

There was in this way of formulating the unit of analysis a further link to older ideas. Karl Polanyi, the Hungarian (later British) economic historian, had insisted on the distinction between three forms of economic organiza­tion which he called reciprocal (a sort of direct give and take), redistributive (in which goods went from the bottom of the social ladder to the top to be then returned in part to the bottom), and market (in which exchange occurred in monetary forms in a public arena). The categories of types of historical systems—minisystems, world-empires, and world-economies— seemed to be another way of expressing Polanyi’s three forms of economic organization. Mini-systems utilized reciprocity, world-empires redistribu­tion, and world-economies market exchanges.
_{— Immanuel Maurice Wallerstein: "World-systems Analysis: An Introduction", Duke University Press: Durham, 2004. (PDF)}

To apply this to much smaller units:

We use the “urban cluster” concept of modern scholarship to investigate the spatial polarization represented by the core-periphery structure of the modern world-system. The focus is on cities within the system and how these are implicated in the development and reproduction of this uneven economic development.
_{— Peter J. Taylor, Michael Hoyler, and Dennis Smith: "Cities", in: Wallerstein (Ed): "The World is Out of Joint. World-Historical Interpretations of Continuing Polarizations", Routledge: London, New York, 2015.}

For going really macro:

The HIE characterizing the current distribution of wealth between countries emerged only gradually before the nineteenth century.

In short, for much of the period between the fifteenth and late eighteenth centuries, the national boundaries of states had not yet become the crucial criteria organizing categorical inequality. We illustrate these patterns, in Figure 3.2.2 with a stylized representation of the three populations that eventually became contemporary Brazil, Portugal, and the United States.

The basic notion represented in Figure 3.2 is that, early on, nation-states were only an incipient marker of inequality, as illustrated in the figure by the dotted line demarcating state boundaries. State boundaries became crucial only over time, illustrated in Figure 3.2 by the accentuation of the line demarcating national state boundaries over the three represented “moments.” On the other hand, other boundaries (cities and towns at one “moment,” or the expansion of empires at another) were probably more significant markers of inequality in the earlier “moments,” illustrated by the accentuated lines representing such boundaries in the figure. These nonstate boundaries became relatively less significant over time, represented by the fading away or even the disappearance of the lines stylistically representing such boundaries in Figure 3.2.
_{— Roberto Patricio Korzeniewicz and Timothy Patrick Moran: "Economic Inequality, Stratification, and Mobility", in: Wallerstein (Ed): "The World is Out of Joint. World-Historical Interpretations of Continuing Polarizations", Routledge: London, New York, 2015.}

For an example of application in the desired context of 'empires of the past':

World-systems analysis has been shown to be a powerful tool for conceptualising and analysing the modern world. I have argued that it has a similar potential for understanding the macro-scale structures and dynamics of the Roman empire and its neighbours, and for facilitating comparisons between Rome and other early empires. A number of preliminary hypotheses have been suggested.

World-systems analysis of the pre-capitalist world demands a sense of history equal to that exemplified by Wallerstein's work. Applications of his thesis to the ancient world must take critical account of his own writings on the subject. Among the many problems faced by prehistorians using the concept is the strong possibility that world-economies of an earlier epoch were simply too weak to generate much inter-regional patterning. More progress may be made with local world-system effects within early states, with world-symbolic systems, and other varieties of exchange system which are not so clearly centralised and in which dominance is less apparent at a regional scale. The very clarity permitted by the world-systems formulation should ensure its continued utility.
_{— Greg Woolf: "World-systems analysis and the Roman empire", Journal of Roman Archaeology, Volume 3, 1990 , pp. 44–58. DOI}