Were the monsters of Greek mythology genetically engineered by a lost pre-flood civilization?

No. That theory is modern men projecting their own technology backward onto the ancient world. It has no support in Scripture or in the historical record, and the Ancient Aliens genre that promotes it is invention from start to finish. No. There is not an ounce of truth to it. What you are describing is a habit of mind more than an argument. Men of the present day look at something old that they cannot immediately explain, and because the only kind of power they can imagine is the kind they themselves possess, they conclude that somebody back then must have had laboratories and gene splicing and machinery. It is easy to do, and it is extremely easy to make television shows out of it and earn millions of dollars. Ancient Aliens is the obvious example. It is all invention. I get the same question about the pyramids, about Stonehenge, about the moai on Easter Island, usually with fallen angels or the Book of Enoch attached. I do not go for any of it. That is myth and legend, and I tell people plainly, do not go there. And the ordinary explanations are not hard to find once you stop assuming ancient men were stupid. Take one of those multi-ton carved stone figures standing upright on the ground. You cannot put it on a cart, you cannot get enough men around it to lift it. But run ropes to the top of the statue so they form a long diagonal, and a team pulling from one side and then the other will rock it so that the right side takes a small step forward, then the left, and the thing walks down the road. The leverage does the work. That is not lost technology. That is rope, geometry and patience, and there is a great deal of that in the ancient world. Now to the hook people usually hang this on: Genesis 6 and the Nephilim. Some people think the "sons of God" were angels who came down, mated with women, and produced a race of hybrid giants, and from there it is a short hop to saying the Cyclops and the centaurs and the Minotaur are folk memories of that. That is all hogwash. The "sons of God" are the godly line, the line that goes back through Seth to Abel, the people of whom Genesis 4:26 says that men began to call on the name of the Lord, two chapters before any of this. Genesis 6 is the story of that godly line intermarrying with the pagan daughters of men and apostatizing. The Hebrew word nephilim comes from the root naphal, "to fall," and it describes the moral condition of mankind at that time, men who had fallen away from God. The notion that they were literally fallen angels in bodily form entered through the Septuagint's choice of gigantes, "giants." There may well have been men of unusual physical stature then, as there were later (Numbers 13:33; Deuteronomy 2:10), but that is a secondary detail, not the point of the passage. The point of the passage is apostasy, which is why God gave that generation 120 years and then sent the flood. I would also ask you to notice who benefits from these theories and why they sell. The reason people want you to believe in ancient astronauts and engineered hybrids is the same reason they want you to believe in extraterrestrial civilizations generally: it makes us not special. If the earth is just one more planet among billions and our civilization is a leftover of somebody else's project, then there is nothing unique about this place, and if there is nothing unique about this place, then the Incarnation is an oddity rather than the center of history. The Christian claim is the opposite. This is the place God chose, the place where Jesus Christ took flesh, the place Scripture says was created before anything else. The Ancient Aliens worldview is not neutral entertainment. It is a story told to displace that one. As for the Greek myths themselves, there is a much simpler account. Men who no longer had the true religion still had a memory of creation, of a fall, of a flood, and of God's dealings with the human race, and they retold those things in distorted form with the gods and monsters of their own making. Legends grow. It is the old telephone game: one man says something, it goes down the line, and by the tenth man it sounds like something else entirely. That happens even to the lives of the saints, which is why I tell people not to believe everything they read there either. It certainly happened to the pagan past. You do not need a genetics lab to explain a chimera. You need human imagination, which has never been in short supply.