As a brief note, while a lot of slaves were imported from West Sudan, East Africa was probably an even bigger source of slaves.
The first thing to keep in mind is that a lot of the people in the Arab world would appear to us as black. I have friends from Egypt and Saudi Arabia who would be considered black people within the American racial system. There have been several studies of Arab genetics suggesting 10% of the gene pool is African in origin, and much higher in some places like coastal Yemen.
Most slaves brought to the Americas were brought to do agricultural labor. They were kept separate from the rest of white society. The bulk of slaves taken t Arab countries were women used for domestic labor, and highly integrated into the surrounding society, A big difference between how race in America and race in the Arab world is that while we had a one drop system, Arabs did not. The children of slaves were usually freed, and were considered Arabs. This integration is a big reason why African ancestry is relatively evenly spread throughout Arab society. There was actually a large population of people in Zanzibar and along the east African coast of the descendants of free locals, slaves and Arab men that were mostly African genetically, but culturally Arab. After independence and the Zanzibar revolution, many of these people went to Oman, and obtained high positions and influence.
Lastly, there were regions where slavery was important. For example, the Zanj Rebellion, led by East African slaves in what is today Iraq, raged for a decade and took the lives of tens of thousands of people. However, mortality rates for slaves tended to be extremely high, and fertility rates tended to be very low. It's hardly surprising that most people taken as slaves chose not to have children, and American slavery was actually somewhat unusual in that so many children of slaves survived to adulthood. The combination of these factors means that the populations that consider themselves black in the Arab world tend to be very small, despite the large influx of slaves from Africa.