Since the booked time for the flight is almost the same time as the nonstop BA (it's actually 20 minutes longer, which is probably accounted for by the slightly more pedestrian pace of the 346 vs the 744
) I strongly suspect it takes a very similar route. I can well understand a desire to fly down the West coast rather than overfly some of the countries on the way - the great circle route pretty much hugs the coast anyway.
In the days of apartheid and sanctions, SAA had to fly out to Ilha do Sal and back again (i.e. no overflight of continental Africa) which added several hours to the flight time. SAA used the extended range 747SP on the CPT route. At the time (before the introduction of the 744 made nonstop LHR-SIN and trans-Pacific flights possible), I believe this was the longest commercial sector.