So what alliances would form as a result of these shifted interests?
Depends how things play out. If the biggest change is shuffling around the colonies in the Horn of Africa amongst the British, French and Italians probably little changes from OTL. But if the butterflies get agitated and the rest of the scramble for Africa is changed then it could affect the formation of the Entente and Italy's membership in the Triple Alliance. Having said that I think really large scale shifts are unlikely when you work it through:
Assuming the French occupation of Aden is about 1869 +/- and not in direct opposition to ongoing British interests there (ie Britain never took Aden or left it/was kicked out well before the French came in) its probably no more than a diplomatic incident at worst (on the scale of Fashoda or Agadir) and maybe not even that. The British instead look across the Gulf of Aden for a port of their own and take over Obock.
If Britian gains Djibouti and OTL British Somaliland (I'm not sure the French would go after it) they will have borders with Ethiopia on about three sides and importantly Ethiopian commerce will likely flow through British Djibouti so it won't tolerate Italian attempts at making Ethiopia a protectorate. So that's my Fashoda analogy. But the Italians almost certainly back down before it gets bad. But that's all the more reason for them to be a nominal member of the Central Alliance so pretty much like OTL still.
That's just one scenario but it seems fairly plausible. There is of course opportunity for greater divergence from OTL depending on the particulars. The big question in my mind is whether the French use Aden as a springboard to further expansion in East Africa. Either it ends up as simply a coaling port like Djibouti or it becomes a major colony and entrepot and thus refocuses French interests to east Africa in the coming scramble for territory.