There is no way in hell leaving the Bishop is by accident. Therefore, it was left there for someone: Conan, Amuro or Rumi.
Of the 3, Amuro did not know what the Bishop is or represented right away, and Conan is not directly related. Therefore, Rumi is most likely the intended recipient.
Ergo, if we accept that Rum killed Kohji, then Rumi can probably be eliminated as a suspect.
If I had to guess, Rumi is probably some sort of agent who became lovers with Kohji. Kohji found out about her secret identity, and hence jokingly asked if she'd kill him. Later, Kohji somehow died in her place or died saving her, which prompt "such a foolish guy."
As to why the Bishop was left behind, it is to taunt the intended recipient.
Of course, it's just a guess.