The original myth has Shamhat taming Enkidu, who then goes to live with Gilgamesh in Ur, the city, after which he dies.
Viewing post in who will you save? who will you serve? comments
He dies much later! It's misleading to suggest he dies after he goes to the city...
He gets in a big fight with King Gilgamesh (who defeats him) and after which they become friends. They go on adventures together and do many great things. When Enkidu dies, Gilgamesh goes on a final quest to discover the secrets of living forever, and possibly return his best friend Enkidu to life again.
I simply said "after which he dies," because I didn't want to go into detail when my main point was the divergence of this game from the part of the myth I did detail. However, good to see you know exactly where you diverged!