If you make a new solid, at least the width of the comp and then move it so that its right edge is in the middle point of your vector object. And then parent this to the vector object, so that when you animate it across the screen, your solid will stick to it.
Make sure the new solid is below the vector object, but above one of the video layers. Then set the video’s track matte to Alpha Matte. The solid’s visibility will turn off and the video will only appear where the solid is.