With the deer antler, the right-handed twin demolished his brother. The left-handed twin died, but he didn't die. He was hurled off the edge of the earth by his brother. In this dark world below the earth, the left-handed twin still lives and reigns.
The right-handed twin lives in the Sky-World and he is content with the world he helped to create. The left-handed twin lives in the world below. He, too, is content with the world of men. He delights in the sounds of warfare and suffering. These two beings rule the world and look after the affairs of men. During the day people have rituals to honor the right-handed twin. At night they dance and sing for the left-handed twin.
Based on this excerpt, it is reasonable to conclude that
the right-handed twin hurt his brother but did not kill him.
the left-handed twin pretended to die but really survived.
neither twin could die because they were immortal gods.
the left-handed twin was immortal, but his brother was not.