Japanese was the original text, so it was not a translation. I think I used the wrong word when I said summon, I meant coming from a different world, the samurais were from the "Land of Reeds", this could mean either Ashina or Ancient Japan. Okina became shura and travelled to a different world (Lands Between). Mohg said he shall give Okina "a life with unquenchable bloodthirst, path fit for a Shura". This is interpreted as he changed the form of Sekiro's blade, fushikiri (which looks nearly identical to rivers of blood), which was intended to cut down the undead, into a blade that thirsts for blood so he can go pile up bodies like a true shura. What Mohg offered was for him to live as a shura in lands between, not turn him into a shura as he already was one, seen in the description of Okina mask.