Are these parallel lines I'm seeing in this image a real pattern on the Moon?
They are not real. 

The images used in the animation use a mosaic of photographs taken by an orbiting satellite, the Clementine orbiter. This satellite has a polar orbit, and so returns images in strips that run roughly north-south. Due to variations in lighting between orbits, when the strips are joined together, there are artefacts at the joins.

The whole moon image from a ground-based telescope doesn't have such artefacts. The lunar orbiter view was used as it covers the whole moon, including the far-side. As the moon orbits Earth, it appears to wobble (an effect known as libration.) By starting with a whole moon map, and then projecting it to a sphere, this libration can be simulated. You couldn't do that with a single ground-based image.