War Pigs is one of the unlockable songs on that game, if I remember correctly, so you will find it eventually in the game. Chris N has been playing that game to review for us so he could say for sure.
If you wanted to hear the original song look for Black Sabbath's Paranoid (this could be very hard to find, however, it was released in the early 70s). It was re-released in 2004 as part of the Black Box set in 2004- this may be your best bet.