For the most part, western authors were the ones who labeled certain historical states as being empires (though some later non-Western historians working under the influence of western education or western historiography did also use such terminology). I am not saying that there are no non-Indo-European languages which have words that are more or less the equivalent of "empire" (I do not know the vocabulary of all languages and could not possibly make that claim) but I am saying that one should keep in mind that much of the classification of certain states as empires arose primarily from "Occidental" historical writing. The designation of states like Benin or Asante as empires was mostly done by Europeans and some of these designations occurred while these states were still existing (this was certainly the case for Benin and Asante). So it cannot be about "African standards" in cases like those, but would most likely have to be about "European standards" for what constituted an empire. If multiple European writers thought these states were empires at some point, they probably were not just determining this by "African standards."
Songhai, Mali, Kush, Aksum, Kanem-Bornu, and possibly Egypt, Ghana, and Gao would have been considered large states pretty much anywhere in the world when they were at their greatest extent, but the reason they were considered empires probably had more to do with the fact that these states had an organized central government that had sovereignty over many diverse peoples, rather than because they met some exact geographic requirement about size. A geographically large kingdom ruling only one group of people who all have the exact same language and culture is really not an empire in the strict sense of the word, while a geographically smaller state in which the central government has political power/influence over numerous different peoples practicing different cultures probably would be considered an empire in most cases.
People still refer to the Assyrian empire, Akkadian empire, Babylonian empire, etc. as "great empires" and these were either the same size as or geographically smaller than most of the aforementioned African states. The "Austro-Hungarian empire", "Carolingian empire" and "Swedish empire" in Europe and some other empires in Asia are still called empires and they were also geographically smaller than some of the largest historical African states (the ones I mentioned in the paragraph immediately above). These states might be viewed as not meeting some people's ideal geographic requirements for what constitutes an empire, but many other people all around the world still describe these states as empires anyway.
And this is besides the point, but I should state this just for the record: if the estimates for sizes of empires given on various internet sites (which mostly derive from estimates in academic sources, presumably) are basically correct, then it would actually be incorrect to claim that Songhai and Mali were smaller than all of the various Indian and Chinese dynasties - the very largest ones were larger, sure, but not all of them, actually.
As for Algeria (which is mostly empty desert, anyway), it is barely larger than the DR Congo, and both countries are larger than multiple historical states from around the world that have been designated "empires", not just those from Africa.
