As Norman indicated, the instrument that Bassekou Kouyate and some members of his group play is the ngoni.

See this article that describes the ngoni and provides information about other West African names for this instrument:The ngoni, a plucked lute from West Africa.

In case the hyperlink goes bad, I'm posting most of that article below:

"Ngoni is the Bambara name for an ancient traditional lute found throughout West Africa. Though typically a small instrument the ngoni has a big sound and a big place in the history of West African music. Its body is a hollowed-out, canoe-shaped piece of wood with dried animal skin stretched over it like a drum.

The neck is a fretless length of doweling that inserts into the body, which unlike the kora (whose neck goes totally through its calabash resonator) stops short of coming out the base of the instrument. For this reason musicologists classify the ngoni as a "internal spike lute."

The ngoni's strings (which are made of thin fishing line like the kora) are lashed to the neck with movable strips of leather, and then fed over a fan-shaped bridge at the far end of the body. The string closest to the player actually produces the highest pitch, and the player plucks it with his thumb, just like a 5-string banjo. This feature, coupled with the fact that the ngoni's body is a drum rather than a box, provides strong evidence that the ngoni is the African ancestor of the banjo.

Instruments of this general construction can be found from Morocco to Nigeria, and everywhere in between. Some are very large, such as the gimbri played the mystic Gnawa brotherhood of Morocco. Others are tiny, such as the one-stringed gurkel of northern Mali. In Senegal the Wolof call it xalam (pronounced: halam) while in the Gambia the Mandinka have a 5-string version they call kontingo. The version played by the Manding griots of The Gambia, Mali and Guinea is typically about two-feet long and has either four or seven strings. Ngoni players can use a variety of techniques and tunings, below are three typical tunings:

[See the article]

In the hands of a skilled griot instrumentalist, the ngoni can produce crisp, rapid melodies, loaded with cross-rhythms and chromatic nuance. The quintessential ngoni player was the late Banzumana Sissoko, perhaps the most revered and beloved Malian griot of the century. Until his death in 1987, could virtually bring affairs in Mali to a halt when he went on the national radio to sing and play his large, deep-toned ngoni. Of course, is was principally Banzoumanas incisive words that won people's breathless attention, but the fact that he played a ngoni is significant. For Malians in particular, this instrument is deeply tied to their sense of history and identity.
In recent years, some great young instrumentalists have developed the ngonis technical range. Perhaps the foremost ngoni modernizer in Mali is Basekou Kouyate of Segou. Basekou's father played the large ngoni, like Banzumana. But like most of the current generation, Basekou gravitated towards the small, high-pitched version of the instrument. Basekou plays in an instrumental Manding music power trio with Toumani Diabate (kora) and Keletigui Diabate (balaphone). All of these players are modernizers who bring in Western and other influences into their music. Since the ngoni remains the most popular traditional string instrument in Mali, there are many other great young players who have made places for themselves within the griot tradition. Among the most sought-after ngoni players these days are Sayan Sissoko, Mama Sissoko and Moriba Koita."

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There doesn't appear to be any etymology link for the name for the West African musical instrument "ngoni" and the name of the Ngoni ethnic group of East/Central Africa. These people came to what is now Tanzania in 1840 "fleeing from "mfecane" (the times of troubles) brought about by the Zulu expansion under their famous King, Shaka."

History of Tanganyika: