Not exactly. It was 2nd and 5, they gained 4.5 yards. One ref, the one on the Redskins sideline, signaled for the chain gang to move so they moved the chains and set the marker to 1st down. The head referee signaled 3rd down and the chains on the Giants sideline stayed where they were and gave the correct down.
Shanahan thought it was 1st and 10 and they threw the ball about 25 yards downfield for an incomplete pass. Then after that play, they reset the chains on the Redskins sideline to correctly indicate it was now 4th and 1/2 yard.
So for Shanahan, they went from 1st and 10 straight to 4th and 1/2.
Then on 4th and 1/2 yard they completed a 4 yard out pattern but the Giant stole the ball from the receiver, which essentially ended the game.