@Hunter-Habib has that absolutely correct. Moreover, I think the impact of that German victory on the budding safari industry as a whole would have been far greater than just rifle choices. Allied defeat in WWI, which was a very real possibility well into 1918, would have meant that Germany retained both German East (Tanzania) and German Southwest (Namibia) Africa. In the same way it lost these two colonies as a result of the war, Great Britain would almost certainly have lost its East African colonies (Kenya and Uganda) to Germany. German influence rather than British would have dominated South Africa. We should also assume the Germans would have also dominated French and Belgian holdings in East and North Africa had they demanded them.
The safari industry really took off in the interwar years. As noted above, that industry was dominated by the British while much German development of rifles and loadings for Africa largely came to a halt. Hence, the rise of all things British, including their concepts of dangerous game loads and rifles. Had our alternative universe occurred, those inter-war American hunters would have been created by a PH named Albrecht rather than Philip. His stopping rifle would almost certainly have been an OU in a new heavy rimmed metric caliber. Safari would now be thought of as very much through the eyes of German culture and norms.
It is likely that would have remained the case throughout the century, because much of the rise of Hitler and the Nazi movement which led to WWII can be attributed directly to the defeat in WWI and the resulting Treaty of Versailles. I rather suspect that might well have been better alternative history than the one we actually experienced. Though, if we hunted Africa, we all would have been studying some German because it would likely be the alternative to English as a universal language - particularly in Africa.
Regardless of history, I think we can confidently predict that the heavy bore SxS would have been a quaint oddity of English gun development while the forum here debated the relative merits of their Merfert and Jaeger OU doubles.
I love SxS shotguns, and my most used double rifle is a Blaser S2 (fortunately without many of the annoying attributes of a traditional design). But an OU really is a superior design. It is inherently easier to regulate and to scope; it is just as fast to reload as a SxS (yes, I know the myth, but you can prove it to yourself with a SxS and OU shotgun); and smaller calibers work just as well as stoppers meaning they would have been a popular option for all game far more than a SxS double is today.
The fact that our alternative world didn't happen changes nothing about the actual merits of various designs - merely what is considered "traditional."