Britain and Germany the major warlords in Europe had colonies 10 East Africa. East Africa was therefore involved because of extended conflicts and suspicion.
There was a lot of suspicion and mistrust since the German and British colonies were adjacent to each. Each country was suspicious that the other would soon attack her colonial interests nearby.
Britain was forced to join the war because of strategic reasons. She wanted to use East Africa to protect her colonial interests in North Africa and the Middle East.
Germany provoked Britain into war well aware that this was the only way she would divert her attention and resources from the war in Europe.
The British wanted to disorganize the German colonies before they could attack the British areas of interest.
Britain and Germany that were involved in fighting had colonies in East Africa. These colonies were therefore under military obligation to provide troops to their colonial masters.
The fighting powers (Germany and Britain) did not have enough troops; they therefore had to run to their colonies for more fighters.
Even before the war started some Africans were already serving in the colonial armies like the Kings' African Rifles, KAR definitely had to fight in the interest of the colonial master.
The colonial powers recruited Africans into their armies with the intention of using them as human shields in the war. The settlers joined the war because they wanted to protect their position in East Africa.