Yes and no Factfinder.
The Watchtower Society has cleverly and misleadingly tried to suggest in the minds of it's adherents that the kingdom has been reigning over the ORGANISATION itself since 1914 without every actually pronouncing this clearly.
Notice the below from jw.org on the subject of the kingdom. Scriptures in Revelation 7:9,14,16,17 are referenced, yet those scriptures do not prove in the slightest that God's kingdom is ruling now. The Watchtower since 1995 has taught that the "great crowd" in Rev 7 are a FUTURE group. The Kingdom is not presently RULING over JW's whatsoever. So, similarly, JW's can only be PROSPECTIVE subjects of that kingdom. Yet JW.org below lying says that the kingdom is presently "uniting" a "great crowd" from all nations when that "great crowd" only forms during the great tribulation according to the Watchtower.
To get around this, notice the deceptive wording used, that "Millions of meek people are becoming subjects of Jesus."
Notice, they are not subjects of the KINGDOM, but subjects of JESUS. It's a subtle but intentional difference. The Watchtower has never overtly taught that JWs are subjects of God's Kingdom!
But in what way are JW's even only subjects of Jesus when they are neither in the new covenant and nor is Jesus their mediator? That's right - the Watchtower Society OFFICIALLY teaches that 99.9% of JW's do NOT have Jesus as their mediator and nor are they in the new covenant or the covenant for a kingdom. Rather, the Watchtower Society has long taught that the only kingdom subjects that Jesus has been ruling over are subjects of the "Kingdom of the son of his love" (Colossian 1:13). The Watchtower says this kingdom of the son of his love has existed since Pentecost 33AD and is only a kingdom of the 'anointed ones', ie, those with a 'heavenly calling'. 99.9% of JW's are disenfranchised from that kingdom.
Furthermore, although the kingdom has supposedly been 'reigning' since 1914, the 1000 year reign of Jesus and the 144,000 has not yet started! So how can there presently be any subjects of the kingdom! The Watchtower Society knows this glaring, gross contradiction all to well, hence their deliberate choice of wording describing JW's as subjects of "Jesus" not subjects of the kingdom.
So contrary to this new publications claim, the kingdom of God is presently ruling over NOTHING? Satan remains the ruler of this world and the dragon's beast still sits on the throne of world authority (Rev 13:2).
Their latest publication asserting that 'God's Kingdom Rules' perpepetuates the grossly unscriptural FALSEHOODs about the kingdom of God, what it is, and when it rules as perpetuated by the Watchtower Society. This serves the elite well in making JW's believe that their membership and support of the organisation is tantamount to membership and support of the kingdom of God.
From JW.org
5. What does God’s Kingdom accomplish?
By means of a global preaching work, God’s Kingdom is already uniting a great crowd of people from all nations. Millions of meek people are becoming subjects of Jesus. God’s Kingdom will protect them when it destroys the present wicked system of things on earth. So all who want to benefit from God’s Kingdom should learn to be obedient subjects of Jesus.—Read Revelation 7:9,14,16, 17.
During a period of 1,000 years, the Kingdom will accomplish God’s original purpose for mankind. The earth will become a global paradise. Finally, Jesus will hand the Kingdom back to his Father. (1 Corinthians 15:24-26) Do you know someone whom you would like to tell about God’s Kingdom?—Read Psalm 37:10, 11,29.