You do not need to complete the Story Mode or enter a cheat code to play as him. However, he is hidden in the character select screen, which leads many players to think he is locked.
The good news is that the issue has been resolved, and Kratos can now be unlocked using a simple workaround. Follow these steps: how to unlock kratos in mortal kombat 9 pc fix
This opens a folder like: C:\Program Files (x86)\Steam\steamapps\common\Mortal Kombat Komplete Edition\ You do not need to complete the Story