Empires, contrary to popular usage, represents a pretty unique definition in a historical context, in which empires are defined as a political states which incorporates many different ethnic groups into one political entity without doing an American style assimilation of said ethnic groups. This incorporation is usually done through conquest.

The Ottoman Empire for instance, is an empire because it conquered Greeks, Arabs, Slavs etc into itself, Tsarist Russia and the USSR were empires because they incorporated Muslim Central Asians, Ukrainians, Estonians etc into the state, similarly, the British were an empire because it had under its control India and Africa and many different peoples through colonization.

In this sense, there are still a few empires in the world today by the traditional definition: the PRC is arguably an empire because of its hold over the Uighur in Xianjiang and Tibet, Russia is one due to its control over non-Russian territories within itself.

I'm no expert in this historical field, but I'd just like to raise a point about about theoretical/ epistemic perspective.

I think it depends on how you conceptualize "empire" and from what viewpoint you think about it. For instance, I take /u/DeSoulis to be offering a classical geopolitical explanation (see Mackinder and R. Kaplan) that's quite ubiquitous and maintains that the international system is characterized by certain entities (i.e. states) that subsume various ethnic or national communities under their territorially defined borders. As with most areas of inquiry, classical geopolitics has been complicated by scholars who take a more critical approach to understanding the discipline and how it may change across time and space.

Another perspective is brought to us by Hardt and Negri in their 2000 book... Empire, in which they understand the term in light of post-modern/ post-Marxist theory. Here's a brief description from Harvard University Press:

Hardt and Negri contend that they should be seen in line with our historical understanding of Empire as a universal order that accepts no boundaries or limits. Their book shows how this emerging Empire is fundamentally different from the imperialism of European dominance and capitalist expansion in previous eras. Rather, today’s Empire draws on elements of U.S. constitutionalism, with its tradition of hybrid identities and expanding frontiers.

Obviously this is a contentious, highly politicized, way of conceptualizing the term--and scholars do not uniformly agree on this definition--but it does offer a brief look into alternate ways of thinking about what empire means in a hyper-globalized world.

Regardless of what you think about Empire, I find it interesting to think about what things like sovereignty, territory, and empire mean in a contemporary context. Even if I don't agree with Hardt and Negri in their various prescriptions, it's important to look into how these concepts change, and to what ends they're employed, and whether or not we need to update our understanding of them to better describe the world around us.