My guess is Rei did kill Shiki but that only happened because Shiki voluntarily allowed herself to be killed by Rei, due to Shiki's feeling prevented her from injuring/killing Rei.
In regard to the ritual, unlike other assassin clans, only one Shiyuu can exist at a time, thus the 'last-man-standing' (or maybe we should call last-girl-standing) in the ritual is the best method. Other members of the Shiyuu clan are simply nameless assassins.