I can certainly see why you would think that from your map, but apparently the mega Kalahari desert extends from the Orange River in So. Africa all the way up into the southern boundries of the Democratic Republic of Congo....
"...The Kalahari Desert - or Kgalagadi, as it is known in Botswana – stretches across 7 countries – Botswana, Zambia, the Republic of South Africa, Zimbabwe, Namibia, Angola and the Democratic Republic of Congo (DRC). It's coverage in Namibia is called a ‘desert' principally because it's porous, sandy soils cannot retain surface water, but in some areas annual rainfall can be as high as 250mm, which accounts for the luxuriant grass cover during good years...."
Kalahari Desert | Namibia
"...The Kalahari Desert is an area of scarce surface water stradding Botswana, Namibia ans South Africa. This is part of the more extensive area which is physio-graphically ans sedimentologically unified, called the Mega Kalahari (Thomas 1984). The Mega Kalahari lies within the trritories of eight countries, from north to south: Gabon, Republic of Congo, Angola, Zambia, Namibia, Botswana and South Africa..."
The KALAHARI transect
"...1n the southern part of Africa the extensive Mega-Kalahari erg extends fiom just south of the equator in the Congo Basin (de Dapper, 1988) to the Orange River in the south..."
Mega Kalahari
The Kalahari Environment - David S. G. Thomas, Paul A. Shaw - Google Books
"...The Kalahari is not a true desert, but a semi-arid zone extending from the Orange River in South Africa to the southern reaches of the Congo...."
African Safari Destinations, Kalahari Desert, Botswana
Kalahari sands extend from the northern Cape in South Africa to the Democratic Republic of Congo.
Routes Travel Info Portal: Kalahari desert - Kalahari xeric savanna ecoregion
The Kalahari, which extends from the Orange River to the Congo, is the largest continuous stretch of sand in the world.
The Kalahari essays
The mega Kalahari can be seen as the orange area in this usda.gov soil map ......as you can see it extends up into the DRC....
Bigger view of map....
http://soils.usda.gov/use/worldsoils/mapindex/metadata/maps/afrorder.gif
Google is your friend.