The Davidic Kingdom of the Old Testament is a foreshadow of the fulfilled Kingdom of Christ.
To understand Christ's Kingdom and his Kingship, we must first understand the Davidic Kingdom.
In the Davidic Kingdom, the Mother of the King was the Queen. The Queen Mother acted as an advocate and mediator between the people and the King. The King would always listen to the requests of his Mother. Being the Queen she also had a place of honor among the people.
Likewise in Christ's Kingdom, His Mother, Mary, is the Queen Mother. She is our advocate and mediator. She petitions to Christ on our behalf. Christ listens to the requests of Mary (evident at Cana) and honors her. The will of Mary and her Son are identical. So too, we should honor our Queen Mother, Mary, as Christ honors her (and did honor her in her immaculate conception). Mary is to be accorded honor above all, second only to her Son. However, she is not to be adored as Christ is. Adoration is for God and God alone. Mary is venerated as the highest created being.
The Davidic Kingdom also had ministers who helped run the Kingdom. So too, in Christ's Kingdom the bishops are the ministers.
"You are those who have continued with me in my trials; and I assign to you, as my Father assigned to me, a kingdom, that you may eat and drink at my table in my kingdom, and sit on thrones judging the twelve tribes of Israel." (Luke 22:28-30)
Just as the Davidic Kingdom has ministers, so to with Christ's Kingdom; and just as David's Kingdom had a Prime Minister, so to does Christ's.
"In that day I will call my servant Eli'akim the son of Hilki'ah, and I will clothe him with your robe, and will bind your girdle on him, and will commit your authority to his hand; and he shall be a father to the inhabitants of Jerusalem and to the house of Judah. And I will place on his shoulder the key of the house of David; he shall open, and none shall shut; and he shall shut, and none shall open." (Isaiah 22:20-22)
And I tell you, you are Peter, and on this rock I will build my church, and the powers of death shall not prevail against it. I will give you the keys of the kingdom of heaven, and whatever you bind on earth shall be bound in heaven, and whatever you loose on earth shall be loosed in heaven. (Matthew 16:18-19)
When Christ was establishing Peter as His Prime Minister, He quoted directly from Isaiah 22. He gave Peter the keys to the Kingdom. Peter is given the authority that the keys represent, just as Eliakim was given the keys.
As Americans, the idea of Queens and Prime Ministers in a Kingdom might sound foreign because we live in a democratic state and do not have these things. In order to understand what is going on in the Bible, we need to study other cultures not like our own.
If people read this in other countries that do have a monarchy, and they are not hardened to the Truth, then they would clearly realize what is going on. They would see that only the Catholic Church has carried on the Kingdom that Christ gave to the Apostles.
When Christ told the Apostles he was given them the Kingdom "that you may eat and drink at my table in my kingdom," the eating and drinking at the table referred to the Eucharist. The very place where we encounter the Real Presence of Christ, the Parousia! The Parousia not only meant a "a coming in glory", but it was also used to describe the coming of a king. That is exactly what happens in the Eucharist. Christ the King comes in glory and is fully present!
The Kingdom of Christ is experienced in the Liturgy!