The 9,3x64 did not exist in the German colonial era, but a 9,3x62 would fit perfectly.
HWL
This is absolutely correct
East Africa...
Wilhelm Brenneke created the 9.3x64 in 1927, but the German share of East Africa, was taken over by the British under a League of Nations Mandate in 1922 after the end of WW I and the Versailles Treaty.
There is ample evidence that the 9.3x64 served well in East Africa, but, indeed, by the time it arrived, Tanganyika was not "German East Africa" any longer but "British East Africa", although technically the British East Africa Protectorate became the Kenya Colony in 1920 and Tanganyika was called the Tanganyika Territory after the British took it over.
I did not mention the 9.3x62 because the OP specifically discussed the 9.3x64
9.3x62 and 9.3x64...
Regarding the calibers themselves, there is little doubt that the 9.3x62 was hugely popular with German colons, reportedly in large part because it was readily available in very affordable Mauser rifles and it worked, but there is also little doubt that it stands at the lower limit of acceptable power for dangerous game, and that the 9.3x64 is considerably better suited as an all-around cartridge for all African game, including dangerous game.
This being said, by the time the 9.3x64 arrived, it was arguably too late, as the 9.3x62 was everywhere and provided acceptable, if not stellar, performance, and the 9.3x64 never developed the popularity of the 9.3x62 with the German in Africa or the .375 H&H with the British in Africa.
7x57 and 7x64...
In a way, the 9.3x64 story in Africa is similar to that of the 7x64 also developed by Wilhelm Brenneke toward the end of WW I (1917). It too never dislodged the 7x57 in Africa after WW I, although it too is a noticeably faster, flatter shooting and significantly more powerful cartridge, but in this market segment the 7x57 was everywhere and provided good performance.
In Europe conversely, the 7x64 proved hugely successful, to this day, where it is the .270 Win / .280 Rem equivalent, while the 9.3x64 did not really succeed in Europe because it was/is needlessly powerful for the largest game (typically wild boar and Stag) for which the 9.3x62 is plenty powerful enough, and it remains to this day a short to medium range caliber of choice.
Tradition vs. performance...
So, the traditional metric battery would be 10.75x68 Mauser; 9.3x62 Mauser and 7x57 Mauser.
The performance metric battery would be 12.7×70 Schuler; 9.3x64 Brennele and 7x64 Brenneke.
PS: actually the 12.7×70 Schuler was such a good design that the Brits copied it and renamed it the .500 Jeffery....