If you can run GoW2 on the PS3 Emulator, you are required to use IGT to time your runs. This is a visual guide on how to install it.

First, right click on LiveSplit and go to "Edit Splits...". Then, on the "Game Name" field, select God of War II:

When you select God of War II, an option to install "IGT for RPCS3" will appear:

If you want to run Challenges of the Titans, go to "Settings" and select the box "IGT for Challenges". After installing the plugin, make sure you are displaying Game Time on LiveSplit:

And make sure the timer on your layout is set to either "Current Timing Method" or "Game Time":

And you're done! After installing the plugin, the timer should automatically start once you start a new game. You don't need to do anything else. You are free to add new splits and change LiveSplit's layout however you like, just make sure the Game Time is visible while running.