On Polyuphemus' island, there are no rules or laws at all. in the eyes of the Greek soldiers (Odysseus included), he violates the (Greek) laws of hospitality. Polyphemus unceremoniously munches on Odysseus' men while holding conversation with Odysseus, not because he was angry or punishing them for entering his cave without permission; he eats them because he sees them merely as food that wandered into his house. He does not offer the "visitors" food or drink because that is not part of his culture, but Odysseus in upset by this. It is the arrogance of the traveler within strange lands that leads to the assumption that the laws back home should be the same laws everywhere else. And that still is in effect today.
This is an interesting question, especially as we contrast the Cyclops and the Greeks in general and Odysseus in particular. The Cyclopes live in a society where there are no laws. They have no civility, no councils, no traditions, and no sense of what is right or wrong. They are cannibalistic one-eyed giants. That pretty much sums it up. Polyphemus is the most famous of them. Part of the reason why they do not need structure is that they have an abundance of food; they land is lush.
All of this is in stark contrast to the Greeks. The Greeks have councils, traditions, laws, and what is very important in the Greek world is hospitality. This is why the whole Trojan War started. Paris stole Helen from the Greeks. It was a huge breech of hospitality. From this perspective, Polyphemus is a barbarian. He eats a few of Odysseus’s men and want to do the same to him. From this perspective, he is the anthesis of the Greek.