Kishida was the other candidate for the Maguro, besides Takaichi, but he wasn't chosen because he tends to lack when the going gets tough... at least nowadays.
But he was still a player, and one that always looks for himself so he was doing his runs around to get on top, he had allied himself with the Kujira.
I don't remember if it was on the condition of joining Kujira as a high-rank member or if it was to take control of Maguro after they killed Takaichi, well... one way or another it failed.
Why Takaichi didn't kill when he has all the right? Dont know, respect maybe, maybe he thinks there was too much death already, and he understands Kishida enough that he doesnt mind overlooking this time as long as he doesnt repeat it again.