I don’t think I explained myself well in my earlier post.
Your complete itinerary must satisfy all the rules, or it cannot be ticketed.
Rule 4(e) concerns allowed intercontinental arrivals and departures.
The continents in your itinerary are:
Europe/Middle East –intercontinental arrivals and departures are compliant – see note 1 below
Africa – intercontinental arrivals and departures non-compliant – see note 2
South West Pacific – compliant
North America – compliant
So, Africa is non-compliant and therefore your itinerary is invalid.
Note 1
For Europe/Middle East, your intercontinental arrivals and departures are:
Departure: DOH-EBB
Arrival: EBB-DOH
Departure: DOH-JNB
Arrival: LAX-LHR
Your itinerary is compliant with 4(e) Exception 3
PS: Europe/Middle East is one continent not two
Note 2
For Africa, your intercontinental arrivals and departures are:
Arrival: DOH-EBB
Departure: EBB-DOH
Arrival: DOH-JNB
Departure: JNB-SYD
Rule 4(e) allows only one arrival and one departure for Africa.
Your itinerary has two of each and is therefore invalid.
FWIW, I too am surprised that BA considered it a valid itinerary.