The fins do cause the rounds to spin once they leave the barrel, punkworks shows it in their High Speed Video. I've seen but cannot share additional video from another independent source that shows that the Rifled LAPCO barrel does impart a spin on a round before it leaves the barrel.
Assuming that out of a smoothbore barrel that they ultimately reach their optimal RPM downrange, they will maintain the orientation they have as they stabilize. While this is not ideal it would help keep the round from tumbling. This lag in stabilization may be a contributor to the spread on these rounds even in an indoor facility from bench-locked marker. The manufacturer also claims that the spinning helps prevent/reduce random vortices from forming behind the round and pulling it off the intended trajectory.
I have several reasons why I think a rifled barrel that successfully applies a pre-spin could improve the accuracy and/or range of these rounds but, I'm waiting for performance testing to confirm it.