There certainly are many adaptations in the light receptors in the eyes that enhance contrast, color sensing, color discrimination as well as feature and movement sensitivity.
In school we usually learn about the cone and rod cells which are color and contrast sensitive in humans. Humans have only 3 types of cone receptors, the record may be 16 types of cone receptors. Many animals have no cone receptors and don't see color. The highly polychromatic mantis shrimp with 16 color receptors mentioned here may devote most of its brain power to motion sensing and little to color or feature parsing.
Motion sensing is not only wired in the brain, but the neural layers within the retina also generate neural signals when motion happens in the eye. In the case of human beings the rod cells generate motion sensitivity.. Individual cell groups can cue to motion in a specific direction before passing off to the brain, which really helps with the reflex time.
All this takes a lot of brain power and the density of the cone cell density is highest in the center of your field of vision.
The density and the neural structure of the retina is highly flexible, adaptable to many configurations. Humans have a circular patch of high density cone receptors, cheetah have a long vertical streak of them which help them track prey when running at speeds over 60 miles per hour.
All this being said, its unlikely that an animal would only see movement, especially a larger on. In Jurassic park, the tyrannosaurus motion only eyes was a dramatic twist - its hard to imagine an animal having such a huge blindspot. Indeed this specific theory is now mostly discounted.