Wikipedia defines an Empire as following:
The term "empire" does not have a precise definition, but is generally applied to political entities that are considered to be especially large by the standards of their time and that have acquired a significant part of their territory by conquest.
When one thinks of an Empire, a large state comes to mind which comprises of multiple cultures, ethnicities and a formidable military. But then when one looks at the Aztec Empire, it all goes wrong. Compared to contemporary and historical empires, one could say that Aztec Empire was not even large enough to be a duchy in Europe or Emirate in Asia. Also neither was it a singular political entity in traditional concept of Empires (but the counter argument here would be the Holy Roman Empire). It comprised of only 117,501 sq mi of area. I asked few friends about it but they disregard the area based on claims that Aztecs had no horses which were backbone of communications and expansion in that era.
My Question is why are they referred to as the Aztec Empire? Why not use more modest and realistic titles of Confederation or Kingdom?