Now that Homefront: The Revolution is available, we know more about the TimeSplitters 2 Easter Egg included with the game.
In the above video from Eurogamer (gameplay begins at 1:00), they give out these details on how to access the arcade cabinet in Homefront that includes two TimeSplitters 2 levels:
Once you reach the Restricted Zone, head to a place called The Bourse (a mission will take you there if you can’t find it). Once inside, ignore everything and head all the way up to the top floor, where you’ll find an offline arcade cabinet. Interact with it and you’ll be able to access two emulated levels from TimeSplitters 2: Siberia and Chicago.
Here’s another video with more gameplay: