It is clear that these two spectres that appear on the ship and play a chilling game of dice for the life of the Mariner represent what their names say they are. Death represents complete death, and Life-in-Death represents a state of death that exists in life, that the Mariner has to suffer because Life-in-Death wins the Mariner, whereas Death wins the life of the sailors, resulting in their deaths. Note how they are described:
Are those her ribs through which the Sun
Did peer, as through a grate?
And is that Woman all her crew?
Is that a DEATH? and are there two?
Is DEATH that woman's mate?
Her lips were red, her looks were free,
Her locks were yellow as gold:
Her skin was as white as leprosy,
The Nightmare LIFE-IN-DEATH was she,
Who thicks man's blood with cold.
Clearly focusing on their descriptions, and in particular the description of Life-in-Death, shows they are deeply suggestive of what these figures represent. The fact that Life-in-Death wins the Mariner, and the way that we are presented with how the Mariner lives--doomed to wander the world and share his story thanks to an uncontrollable compulsion--shows the life-in-death that he has to endure as his punishment.