Minos was not Greek. Rather, the historical Minoans discovered barely a hundred years ago by Sir John Evans were certainly not Greek, but–linguistically and ethnically–related to the Near East. But for all that we know of Minoan civilization, i.e. not much, they have always been an integral part of Greek, and therefore European, civilization. As late as Plato, the Greeks remembered Minos as the great king of a seafaring people, so powerful that he rid the sea of pirates and forced the Athenians into paying a yearly tribute consisting of seven young men and seven maidens. It is on Crete that Zeus was raised, protected by the mysterious Curetes, and it is on this island that he brought desguised as a bull the Phoenician princess Europa. Crete is legitimately the birthplace of Europe in this respect.
Even today this mysterious people remain in our legends the starting point of Western culture and civilization, although we cannot be certain of anything. Art historians have often seen, and still do, the Harvester’s Vase as a precursor of Classical Greek art, because the unique and distinguishing feature of the vase was the representation of a harvester singing, mouth wide open, with especially the depiction of the ribs inflating as the harvester inhales in order to sing. This feature, never seen before in art, is commonly thought as the beginning of a naturalist view of art which would result in the heights of the Classical age. How much influence this isolated work–we know of none others like this in Minoan Crete–really had upon later generations, we cannot be sure. It is certain, however, that Minoan artistic style influenced the Mycenaeans, who were Greeks–and perhaps, through them, the later Greeks of the Archaic and Classical ages, though the direct link between Mycenaean and Archaic Greece seems virtually lost after the fall of Mycenaean palaces. It remains nonetheless that the Minoans were extremely curious about the environment that surrounded them, giving their art a refreshing, living touch seldom seen elsewhere–and which also contributed to our idea of the Minoans as a peaceful people, even though we once again know little about that.
I wonder about your sources for this post, because mine seem to disagree a little. There are periods of the Minoan civilization and it is known that from some time and after (at least at the time of the destruction of the palace in 1400) the palace was controled by Greeks and there was an influence from the Mycenean to the Minoan civilization (not only the opposite) as is proved by the emphasis on arms at burials, the adoption of the Mycenean style of graves and the ceramics – influences that came from the Greek mainland (Bury-Meiggs, History of Ancient Greece, v. 1). But the most impressive evidence came with writing. Michel Ventris proved that Linear-B writing is a pre-homeric form of Greek.
It all depends indeed on the period one speaks about, though even this needs not be an exclusive boundary. In the period before the destruction of the Cretan Palaces around 1500-1400 is one that sees strong Minoan influence in the Aegean–although we don’t know for certain about the nature of this influence; was it political and military, economic, and/or cultural? There appears to have been Minoan ‘colonies’, at the very least zone of influence, in the southern Peloponnese. A more general aspect of influence comes from art, especially the fresco painting, directly inherited by the Mycenaeans from the Minoans, and which underwent little change over the centuries. We may almost speak of the reverse situation after the Mycenaeans invaded the island (Warrior Graves, etc.). This did not mean that all Minoan influence ceased. A fascinating example of this would perhaps be in mythology. Cretan mythology preserves the remembrance of a tomb for a god, presumably Zeus– a very un-Greek concept. Given the situation of the world in the II millenium B.C., such two-way cultural exchanges are not surprising at all, and may have had lasting results. Two worthy references would include Lord W. Taylour, The Mycenaeans, and J. Lesley Fitton, Minoans.
It is indeed impressive that an archaic form of Greek was written with a non-alphabetical script, which we can read, well before Homer. This stretches Greek history in a direct continuous line over almost 3400 years…