He is in loco parentis, the man who is not the natural father but who is in the position, with its duties of care, of any parent who is with the child. The natural father was someone else, so we could not call this man the parent, only the step-parent.
Unfortunately it is the cohabitee, the step parent, who is always the most likely to kill or act cruelly to the child. There must be some primitive instinct which says that the only child in the house has to be his; like male bears killing cubs fathered by another. And there is not, perhaps, the natural bond that a natural father has.