A very basic definition of empire would be a political entity where a single leadership (e.g. an Emperor) exercises control over many different nationalities/ethnic groups.

Alternately, an empire could be described as a state or political entity that has subsumed multiple formerly independent states into one single leadership.

If we look at the example of the Achaemenid Persian empire, it fits both of those definitions. The Achaemenid Shahs ruled over an expansive realm that included Egyptians, Lydians, Babylonians, Medes, Ionian Greeks, Indians, and others. Also, Egypt, Babylon, Lydia, and others had formerly been independent states before being conquered and incorporated into Persia.

For another example, we could look at the Qin dynasty, which conquered six other kingdoms of the Warring States period. I'm not a scholar of china, so I can't say whether China scholars would say ethnic distinctions existed in the warring states, but at minimum the Qin dynasty satisfies the second definition. The Qin dynasty is generally considered the first of the Imperial dynasties of China.

So, to answer your question, Benin, Mali, Oyo and Abyssinia/Ethiopia are called empires because they satisfy both of those definitions.

the Mansas of Mali exercised control over a wide swath of the West African savannah, conquering or forcing into tribute many different kingdoms and ethnic groups.

Similarly, Ethiopia was and is a state with many ethnic groups. The Negusa Nagast (lit. "King of Kings") ruled over many quasi-independent provinces, and over the course of several hundred years, the cultural and political influence of the Ethiopian monarch expanded over formerly independent or even hostile states like the Sultanate of Ifat.

Again with Benin, it started out as a small Edo-speaking state. Starting around 1440, under the Oba Ewuare, the armies of Benin began conquering neighboring Ijaw, Ibibo and Igbo speaking cities, and by the 1500s Benin was briefly in control of Atlantic ports as far west as Accra. Though through the 1500s political rivals and changing trade meant Benin lost control of those ports and her realm diminished.

With Oyo, it is again a story where an expansionist Yoruba speaking state first conquers independent Yoruba states like Ile-Ife towards the end of the 1500s, and then goes on to conquer the Fon-speaking Kingdom of Dahomey.

So, all of these states are called empires because they satisfy a simple working definition of an empire as an expansionist multi-ethnic state. No, they don't really resemble the British or French or German empires of the late 19th century, but then again the Qin dynasty doesn't really resemble those examples either.

Do African people have different definitions of the title "Empire" ?

It was European historians from the 19th or 20th century who are responsible for applying the term empire. Part of the reason for applying such a term is categorization of eras. Benin before 1440 could be categorized as "benin kingdom", 1440-1897 as "imperial benin" and after 1897 as the colonial period. Ditto for other examples.

It's not because African people think "empire" means something different.