The Namibia Professional Hunting Association's website says:

Firearms

Smallest calibre 7 mm.
Minimum energy (Eo - muzzle velocity): 1350 Joule for springbuck, duiker etc.
2700 Joule for hartebeest, wildebeest, kudu, gemsbuck, eland etc.
5400 Joule for buffalo, elephant, rhino etc.

No solid point cartridge is allowed to be used on antelope or any other species.
!! Handguns and automatic weapons are prohibited. !!

which I alway interpreted as prohibiting semi-autos. If you email them they can probably clarify it for you. If not, I know people I can ask.

Benelli did a show there with the R1 when it came out, and I was one of those who wondered how they were able to do that.