Alma clarifies that the temporal death of which he had spoken earlier is precisely the same death that came upon Adam and all of mankind. Because of Adam we all die a temporal death.
The next thing Alma does is provide a context for earth life. This life is the "space grated unto man in which he might repent." What we do in this life is prepare ourselves to receive the joy of God, a state that will come after the resurrection, and by implication, after the judgment.
What Alma does not say explicitly we must imply. Alma implicitly suggests that it would have been possible for God to cut off mankind right at that point. After the Fall, there could have been an immediate cessation of the earth, and then all would be condemned, since they were all subject to death. It is only in the mercy of God that the earth life is allowed, and it is the purpose of that life to prepare ourselves for the next state of life, that "endless state."