I understand why you might think there is no actual tangible 1,000 year reign of Christ on earth but I think you are wrong. Daniel 7:13-14 are yet future. The "kings" you cite from Daniel 2:44 are also future.
Christ has not yet returned but He will soon as we learned from Hosea that there would be a 2,000 year gap between His earthly birth and His Second Coming. We are at approx 6,000 years of Biblical recorded history. An additional 1,000 years is needed for divine completeness so, it makes sense for there to be a 1,000 years of peace under Christ's reign before the final eternal heaven state.
Christ has not yet returned but He will soon as we learned from Hosea that there would be a 2,000 year gap between His earthly birth and His Second Coming. We are at approx 6,000 years of Biblical recorded history. An additional 1,000 years is needed for divine completeness so, it makes sense for there to be a 1,000 years of peace under Christ's reign before the final eternal heaven state.
Daniel 7:13-14 I saw in the night visions, and, behold, one like the Son of man came with the clouds of heaven, and came to the Ancient of days, and they brought him near before him. And there was given him dominion, and glory, and a kingdom, that all people, nations, and languages, should serve him: his dominion is an everlasting dominion, which shall not pass away, and his kingdom that which shall not be destroyed.
Acts 1:9-10 And when he had spoken these things, while they beheld, he was taken up; and a cloud received him out of their sight. And while they looked stedfastly toward heaven as he went up, behold, two men stood by them in white apparel;
Peter's sermon. Christ was already on the Davidic throne in heaven...
Acts 2:29-36
29 Men and brethren, let me freely speak unto you of the patriarch David, that he is both dead and buried, and his sepulchre is with us unto this day.
30 Therefore being a prophet, and knowing that God had sworn with an oath to him, that of the fruit of his loins, according to the flesh, he would raise up Christ to sit on his throne;
31 He seeing this before spake of the resurrection of Christ, that his soul was not left in hell, neither his flesh did see corruption.
32 This Jesus hath God raised up, whereof we all are witnesses.
33 Therefore being by the right hand of God exalted, and having received of the Father the promise of the Holy Ghost, he hath shed forth this, which ye now see and hear.
34 For David is not ascended into the heavens: but he saith himself, The LORD said unto my Lord, Sit thou on my right hand,
35 Until I make thy foes thy footstool.
36 Therefore let all the house of Israel know assuredly, that God hath made that same Jesus, whom ye have crucified, both Lord and Christ.
Are you going to say the above passage is still future?
As for Daniel 2:44, the kingdom was to be set up through Christ's first coming during the time of the Roman Empire. Thus that has been fulfilled.
Christ even stated that His kingdom had arrived...
Matthew 12:28 But if I cast out devils by the Spirit of God, then the kingdom of God is come unto you.
Mark 1:15 And saying, The time is fulfilled, and the kingdom of God is at hand: repent ye, and believe the gospel.
Notice that He didn't say "the time will be fulfilled at my second coming to establish a kingdom", rather He said "the time is fulfilled"; it has come.
So there's no indication of a literal 1,000-year reign of Christ on earth in the bible.