I heard about the story of the game in an interview,so the game is supposed to take place in an alternate reality were Churchill was hit and killed by a taxi,and so was unable to make the speech that motivated the country to win the Battle of Britain.
Because of this event Hitler was able to succesfully take Europe and the United States were never drawn into the war.
As we were not in the war we had none of the technological advances that were in the war and the Nazis had that tech,a decade ahead of ours and so invades the United States.
You play as a construction worker trying to survive and rebel against the attack and later in the game,a Nazi occupied New York.