Alma uses the idea of physical death to create a way of describing the second effect of the Fall. The physical death is a separation of body and spirit. He now describes a second "death." This "death" occurs at the time of the judgment when the unrepentant man stands before God. God righteously precludes such a man from the His presence. This separation of man from God's presence is called a "second death."
"Things pertaining unto righteousness" at this point would be the acceptance of the repented soul into heaven. That is the location of righteousness. Where the unrepentant will go is not part of that realm, it is a realm of unrighteousness. Alma further describes that location in the next verse.