I agree with you not NEEDING to play Ghost of Sparta but at the same time... (Ghost of Sparta spoilers below, but come on, its been 3 years just read it).
You freaking get to understand that Zeus is litterary your father and the whole Son-killing-Father theme is something thats common in Greek mythos (Just look at Zeus and Cronos). Its the whole "marked warrior" prophecy, the prophecy that the king of gods will fall to a marked warrior. Add that to the fact that Zeus basically kills Kratos' mother (or err makes her into a giant monster for telling Kratos that Zeus is his father which forces Kratos to kill her) and that Ares/Athena are tasked to take away the "marked warrior" which actually is Kratos but they accidentally took his brother. And after all of that, they offer to take away his memories but he doesnt want to forget what they have done to him. Kratos killing Thanatos essientally makes him the God of Death and as Zeus in cameo puts it "The destroyer of both worlds".
So yeah, it does add rather much.
