The pistol veer provides a great complimentary play to the pistol zone read. The zone read typically is a play that will hit from the frontside of the play all the way to a cut back on the backside. The veer looks like the zone initially in many ways, but the running back is never attempting to take the ball across the midpoint.
The offensive line on the play side(which appears many times to the defense to be the backside of the play, is now down blocking aggressively rather than zone blocking. We basically maintained our zone rules on the backside of the play.
Many times the gun or pistol veer is misidentified as zone because of the similarity of reading the defensive end. For the quarterback, there really is no difference in the read of the end man on the line. The footwork will vary slightly, but his decision remains the same. If the end closes, he will keep. If the end sits, he will give.
I suspect that the play is being run in the NFL as well. In 2012, the Redksins ran a read option play in which the offset back next to RG3 received the hand off and never looked to attack across to the other side of the play. The TE (aligned as a tackle) arced up to the linebacker, which definitely tells us that it was not zone blocking. RG3 and the pistol back ran a pitch course. The play is illustrated below.
While the play does not hit as quickly as the traditional under center veer, it does seem to hit a bit quicker than the zone play because the back is going downhill immediately after receiving the ball. Here is a video from a one back set:
It seems that the pistol veer is being utilized more on every level and is gaining popularity. Here are a list of resources that give more details on the play: