My question is how can the Second Coming of our Lord Jesus, after the seven-years of the tribulation, mark the end of the gentiles when Egypt, Iraq, Lebanon, Syria, Saudi Arabia, Yemen and the Palestinians will all be alive and well during the Millennium?
I don’t believe all the nations you listed will still be around in the Millennium. For example, while Egypt and Assyria (not Syria) are mentioned in a millennial context (Isaiah 19:24), Lebanon, which was originally part of the Promised Land, will be so again. Babylon (Iraq) will never be inhabited again (Isaiah 13:19-20), and the Palestinians never were a people.
But here’s the answer to the important part of your question. It’s not that there will be no more Gentiles. It’s that the “Times of the Gentiles” will be over. They began when Babylon conquered Judah in 605-586 BC and will end at the 2nd Coming. (This is symbolized by the statue described in Daniel 2.) During that time there’s always been a gentile Kingdom superior to Israel in the World. During the Millennium Israel will once again be the pre-eminent Kingdom on Earth (Isaiah 2:2-4).