Well, it is important to know that the borders of Ethiopia in the Early Modern period (~1450 to ~1800) were far different from the borders of the modern Ethiopian state. As a shapshot, take a look at this map of the situation in 1510 compared to a map of modern ethiopia, you can see that areas which had been parts of Adal, or the Ajuuraan sultanate, or Oromo lands are part of modern Ethiopia.

Again, that first map is only a snapshot of the situation in 1510, and the borders of Ethiopia expanded and contracted quite a bit in the period from 1450-1800 due to wars with Ifat and Adal, the Oromo invasion, and the protracted chaos of the Zemene Mesafint. But, the modern borders of Ethiopia are the product of an imperial project that occurred in the second half of the 19th century. The "core" of early modern Ethiopia was a portion of the highlands that occupies 40-50 percent of the area of the modern state of Ethiopia.

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With that qualification out of the way, let's look at some other African states in that period from 1450-1800.

The beginning of our time-range is coincidentally very close to when the Songhai at Gao broke away from the hegemony of the Mali Empire. By 1500, the Songhai empire would an area greater than 1,400,000 km^2, which is larger than the area of modern Ethiopia. At the same time, Mali did not simply disappear, but continued to control an extensive but diminished territory, and would bounce back to a small extent in the mid-16th century.

Elsewhere, we can also look at the Sennar Sultanate in the upper nile, in the area that is now the Republic of Sudan. If you go back to that first map, you can see it on the map marked as the Funj Kingdom. Sennar sultanate (from the capital at Sennar) and Funj Kingdom (from the Funj ethnicity) are different terms for the same political entity.

There was also the Bornu state, centered around Lake Chad. here is another map which depicts Bornu, Sennar and Ethiopia all in 1750.

Of course, those three examples all exist within the sudanic region of Africa. Their environment was a savanna and semi-desert plains that strongly favored cavalry warfare, and allowed sprawling trade and tribute networks based on river and camel transport. Early modern Ethiopia is not directly comparable to these states, because it existed in a mountainous highland environment with much more difficult transport options.

We can also look at other states in Central Africa such as the Kongo Kingdom, the Luba empire, the Lunda commonwealth and the Maravi kingdom which also controlled territories not quite as large as Ethiopia, but certainly larger than Asante, Buganda and KwaZulu.

In short, the answer to your question is that Ethiopia was not an unusually large state. The Songhai empire was actually larger, and there were other states that controlled territory of similar area to early modern Ethiopia.