A short, hand wavy, description:
When the arc forms, hopefully on the right side near the teflon, it creates the B field (out of the page). Then the moving electrons (up) experience the force you described ##\vec F=q \dot {\vec r}\times \vec B## (to the right). So that arc is propelled to the right and pushes a bunch of teflon bits out with it. The arc extinguishes when it's source discharges, and then the cycle repeats.
I like to think that the force is created to oppose a change in the magnetic flux. For a given current amount, the flux can be reduced by increasing the loop area, i.e. pushing the arc away.
This is also how rail guns work, if you want to look into those too.