Out of Play with Rounding Runner

With no runners on, the batter (B1) grounds to the shortstop. The shortstop fields the ball cleanly, but the speedy B1 is nearly at first base, so the shortstop does not throw to first base.
 
However, B1 makes a wide turn into fair territory over at at first base. The shortstop sees the turn and throws to first base in an attempt to catch B1 off the base. The shortstop's throw sails out of play. 
 
Since this is the first play by the defense on the batted ball, what base is B1 awarded on the ball thrown out of play?
 
Call
When a live thrown ball has become dead... if every runner, including the batter-runner, has advanced one base at the time of the first play, the award is two bases from the time of the throw (NF 8-3-5). In the play below, B1 is awarded third base (two bases from the time of the throw).
 
In the play below, the PU is responsible for determining when/if the ball goes
out of play. The BU is responsible for the batter-runner at any of the bases.