The binding ends in our world but not the reigning.
According to revelation chapter 20 the binding ends when satan is released in verse 7 and that may of already happened. The reigning ends at the end of our world when the rest of the dead rise see verse 5 which we see happens in verse 12.
I see it as Satan being bound from gathering the nations to destroy Jerusalem and I see the Galatians 2:9 agreement that James, Peter, and John were to go to the circumcision, as something that was never rescinded.
So I come to the conclusion that Revelation was written to the circumcision, meaning that those of the circumcision who were beheaded lived and reigned for the thousand years. Saved Gentiles also live and reigned but I don’t think they are in view in Revelation 20. I see the end of the old covenant circumcision happening in 70AD, when the nations (Gentiles) surrounded the camp of the saints (Jerusalem) and fire came down (in judgment) and devoured them (those who didn’t flee).
As far as “the rest of the dead” there are several possibilities. Luke 9:60 says let the dead bury their dead, and Luke 17:30-31 says that the Son of man is revealed in the day that they are to flee.
When I put these verses together I come up with the dead having Christ revealed to them which causes them to flee and live after the thousand years are finished, just prior to Satans little season.