Is God of War based on a true story

Not exactly. It is loosely based around Greek mythology. Some differences between the actual Greek mythology and the God of War story is that Kratos was not Zeus' son. Kratos, along with his siblings, served as a retinue, a small army you could say, for Zeus. And Kratos was never actually involved with Ares and Athena. A similarity I found is that Typhon was actually trapped in a mountain, Zeus did that. I hope that answered your question.