Has the prophecy about the root of Jesse reigning over the Gentiles been fulfilled?
The prophecy that a root of Jesse would rise to reign over the Gentiles and that Gentiles would trust in Him has not yet been fulfilled. According to the context, it never happened in the past, but it is going to happen. This future fulfillment connects Jesse, David, and Christ.
Les explains that Isaiah wrote there shall be a root of Jesse, and he that shall rise to reign over the Gentiles, and in him shall the Gentiles trust. Jesse was the father of David, and Christ is considered the son of David, so the connection runs from Jesse through David, Solomon, and the whole line of Jewish kings. Les notes that this prophecy never happened in history, but it is going to happen in the future. Even though God dealt primarily with Israel from Abraham until Acts, He did not forget the Gentiles, though He could not deal with them until Christ went to the cross.
And again, Esaias saith, There shall be a root of Jesse, and he that shall rise to reign over the Gentiles; in him shall the Gentiles trust.
And in that day there shall be a root of Jesse, which shall stand for an ensign of the people; to it shall the Gentiles seek: and his rest shall be glorious.