In mammals, the muscles on the sides of the mouth and around the mouth opening in some, but not all of them, form muscle leverage that takes the place of the protractor adductor (jaw closer and muscles that help pull the jaw forward) functions of palatal muscles, and share adduction (closing) loading for the temporal muscles, due to the rear of the mandible having been "lost" (it's shrunk and becomes part of the ear bones). Reptiles for the most part never lost this equipment, and even stem mammals like Dimetrodon have functionally "reptilian" jaw muscles and bone arrangements. The palatal muscles are large, not vestigial or associated with a small mobile structure near the ear designed to stabilize the jaw.
In mammals, a special set of muscles developed in some groups to take up the loss of those muscles that helped the jaws close, and these muscles are associated with the lateral temporal muscles adjusted to inserting onto the dentary bones -- because there are no other bones of the lower jaw anymore. No other animal has such a muscle arrangement: it's simply not necessary, and if it were plausible to assume they existed, there would have to be extraordinary evidence for their existence. To date, no such evidence has been proven to connect the muscular "cheek" to an animal and the bones that underlie it.
Thus, the muscles form a necessary function of helping close the jaw; there is no peculiarity to which their function is necessary for a style of eating. They are present in meat eaters, plant eaters, bug eaters, whales, etc. The masseter types of muscles are merely useful for closing the jaw in a efficient manner, and so they remain selected for. "Chewing" is a dietary function principally of the teeth, and in those dinosaurs for which "chewing" has been inferred, the process is often different from typical vertical mashing or side-to-side stroke-based oral processing, as seen in elephants, for example. Moreover, the muscle components in reptile jaws from which "masseter" like muscles might arise has no necessity for being anywhere near the dentary, as there is plenty of space, and no positive inference to suggest otherwise, for the muscles at the back of the jaws. Indeed, almost all muscle reconstructions for framing the jaws only these back-of-the-head temporal/palatal muscle sets are needed to explain most, if not all, of the muscle efficiency needed to explain tooth wear in hadrosaurs, ceratopsians, ankylosaurs, etc.
As for food processing, no one has ever argued a model by which food would fall out and the animal starve should it not possess some skin-based or muscular structure on the sides of its jaws anterior to the muscles. The fact that food regularly falls out of the mouths of animals with such structures, it seems hard to really make such an argument, but of course, it would have to counter how mere lips could not achieve that effect, given that lip-like oral tissues are the null condition for reptiles and mammals alike.