Perhaps not an answer to your question, but I wonder what your definition of an empire is.

Stephen Howe, in Empire: A Very Short Introduction, posits this definition: A large, composite, multiethnic or multinational political unit, usually created by conquest, and divided between a dominant centre and subordinate, sometimes far distant, peripheries.

Now, I can't comment on the examples you name as they are not my field of expertise, but even in this definition large is a relative term. The Habsburg Empire, for example, was not particularly large compared to the Mongol Empire or the Chinese one, in size and especially in economic and demographic terms.

The other factors besides size might very well fit the examples you give. I'm quite certain any resident experts will agree that the Aztec Empire was certainly composite and multi-ethnic or multinational with a dominant centre.