No it doesn’t the actual text you posted yourself says thousands years not millennium
A thousand years is a millennium.
Christ reigning does not start nor end with this time frame of 1,000 years.
The time frame is for those reigning with Christ. The time frame is not Christ's reign, because that has been all of creation, not just the last millennium.
So, yes after these ressurected humans have reigned a 1,000 years. After Satan has been bound a 1,000 years. After the Millennium will Satan be loosed and deceive many.
Revelation 20 is not about a reign of Christ. It is about a reign with Christ. Since these humans are not in heaven, this is a millennium on earth. The church has already been reigning with Christ in Paradise for almost 1993 years. That is almost 2 millennium. So obviously not about Revelation 20 at all which is only 1 millennium, and on earth, not in Paradise.
The literal Amil position would be a new space race where billions of wicked storm the gates of heaven, since that is how they interpret Revelation 20. That is where Christ is currently reigning from, with the saints in Paradise. That is the only central location of any camp of saints. There is no current central location on earth with a camp of saints. The saints are scattered all over the earth, in nearly every local of humanity. No long treck to find a central location per Revelation 20, is even necessary.
Last I checked, "with" means in close proximity. That would be the point in Revelation 20. Not every one reigns with Christ in that camp of the saints. There are millions of souls redeemed throughout the earth in many nations during the Millennium.
Not even all of Israel will reign with Christ, just the 144k. There is only one throne, and the camp of the saints, the beloved city, where that throne is located. In Paradise there are many thrones.
"And I saw thrones, and they sat upon them, and judgment was given unto them."
These thrones were already there, they did not "poof" into existence that moment. There are not thrones set up on earth. These would be current thrones already set up in heaven. Going by Amil belief, already there in the first century when their millennium started. I would not argue that they have been there as Paul claims we are seated in heavenly places even in the first century. Are not thrones something to sit on since the Cross physically opened Paradise for souls in God's permanent incorruptible physical bodies?
Seeing thrones and souls is symbolic terminology, yes. Thrones are literal seats showing judgment is given. But thrones represents those souls sitting in judgment just as well as souls being judged represent a physical body that is now permanent and without fault, ie incorruptible. That is the judgment handed down.