Edited: Author's note - this answer quotes and answers an earlier version of the question and may be slightly out of date
The short answer to your question is that this should be understood and translated as"Kingdom of God," but this then implies that Jesus is royalty.
The Kingdom Theme of Matthew
The longer answer is that Matthew has a theme which explores the Kingdom of God and explains to readers that this Kingdom has come, but in a very different way than they were expecting. This begins from the outset with a genealogy fit for nobility and royalty. Anthropolgist Dr. Richard Rohrbaugh points this out in his lecture before the Biblical Archeology Society stating,
I spent some time living in the little Palestinian village of Beit Jala in the West Bank doing research. My primary area of interest is peasant studies and in living in Beit Jala, I discovered that when I would be introduced to peasants they would often immediately tell me their genealogy. For most peasants it's only three generations long: me, my father, and my grandfather. Maybe my son - Maybe four. Sometimes in an oral setting like that they will go back and add the eponymous ancestors of the community - Abraham Isaac and Jacob.
Genealogies are, if you will, a kind of a map for the whole community - describing exactly where in the scheme of things you fit. Among non-literate people (which in antiquity was about ninety-six percent of the population); among non-literate people genealogies would be very short. Only upper class wealthy people have written genealogies. And you understand that the longer the genealogy, the better? Because it means you're from old money not new money. You understand?
...What I find interesting is the genealogy in Luke - It goes all the way back to “son of seth, son of Adam, son of God”. That is, it traces it to the beginning. That's the longest genealogy possible. Do you understand that in honor claim is being made? In fact we know from Roman texts that people in the Roman world who did become newly rich and wanted to move up the social ladder hired genealogists to create fictive genealogies for themselves and there were a few stars in the pantheon of Roman ancestors they all wanted to be associated with. For a fee, you could get that association. Now you have the map that tells everybody where you fit in the pecking order of things and that had an enormous impact on your life.
This is then followed by a visit from the Wise Men - they would generally be advisers to a king. Instead of seeking Herod, they seek Jesus - the King who brought the Kingdom. They give Jesus gifts fit for a king.
Herod, then recognizing a threat to his throne seeks to have the new king killed and the family flees to Egypt.
One important role in the royal court was the role of the Herald and John the Baptist acts as the Herald through his preaching to introduce the Kingdom of God by preceding and introducing the King before Matthew details Christ's ministry. The scene with John the Baptist culminates in the Baptism of Jesus which acts as a coronation ceremony in which God himself abdicates the throne in 3:17
And a voice from heaven said, “This is my one dear Son; in him I take great delight.”
Jesus then sets about establishing his Kingdom on earth in a most unexpected way: through his healing ministry.
What is the historical origin of this theme?
In his excellent answer to a question about why Jesus heals a blind man twice in Mark 8, Matthew Miller notes
The title “Christ” in the mind of the Jews carried with it all sorts of expectations which were inconsistent with the suffering message of Jesus. The disciples believed that the Christ was going to be an earthly king, a conquering hero, a military leader who would kick the Romans off Jewish soil. But Jesus understanding of this title was quite different from Peter’s; he viewed his mission as one of suffering and death for the sins of the world. Jesus gathers his disciples and teaches them what it means to follow him.
And he is 100% correct in this note. Matthew is co-opting this expectation and using it as a framework for presenting his gospel to show his readers that Jesus is in fact a King and a savior - just in a very different way than they expected. But what is the origin of this expectation? As it turns out this expectation has it's roots in the Gospel. The word Gospel means "Good News" and has it's origins in the Hebrew word מְבַשֵּׂ֥ר (basar) found in [Isaiah 52:7]:
How beautiful on the mountains are the feet of those who bring good news,
who proclaim peace, who bring good tidings, who proclaim salvation, who say to Zion, “Your God reigns!”
This word מְבַשֵּׂ֥ר (basar) is most frequently used in reference to the good news of message of a successful military campaign. This accounts for the usage of the word in 1 Samuel 31:9; 2 Samuel 1:20; 1 Chronicles 10:9 and Psalm 68
1 Samuel 31:9
They cut off Saul’s head and stripped him of his armor. They sent messengers to announce the news in the temple of their idols and among their people throughout the surrounding land of the Philistines.
2 Samuel 1:19-20
The beauty of Israel lies slain on your high places!
How the mighty have fallen! Don’t report it in Gath,
don’t spread the news in the streets of Ashkelon,
or the daughters of the Philistines will rejoice,
the daughters of the uncircumcised will celebrate!
1 Chronicles 10:9
They stripped his corpse, and then carried off his head and his armor. They sent messengers throughout the land of the Philistines proclaiming the news to their idols and their people.
Psalm 68:1-2, 11-12
God springs into action! His enemies scatter; his adversaries run from him. As smoke is driven away by the wind, so you drive them away. As wax melts before fire, so the wicked are destroyed before God.
The Lord speaks; many, many women spread the good news. Kings leading armies run away—they run away! The lovely lady of the house divides up the loot.
It is no wonder then that when interpreting the Prophecy of Isaiah 52 which Jewish Leaders believed prophesied the coming Messiah Jews at the time of Jesus were expecting a Military leader to overthrow the Roman government and end the Roman occupation. This accounts for many of the objections and criticisms by the Pharisees of Jesus as the Messiah. He wasn't what they were expecting - and Matthew has set out to correct that notion by demonstrating that he was a King and leader bringing good news - just not via earthly, military means.
(consequently, another use of this good news was in regards to the birth of a son - Jeremiah 20:15)
So we can see from the above context, as well as the context of Matt 12:25-26 that the βασιλεία τοῦ Θεοῦ (Kingdom of God) is a technical term fitting into the theme of Matthew which refers to the βασιλεία τῶν οὐρανῶν (Kingdom of Heaven -- Matt 3:2; 4:17; 5:3,10,19-20; 7:21; 8:11; 10:7; 11:11-12; 13:11,24,31,44,) that Jesus is now establishing on earth in starting in Jerusalem. The Gospel of Matthew's purpose then is to demonstrate to readers exactly how Jesus has set about extending his kingdom of οὐρανῶν (Heaven) and the ways in which Jesus brings the βασιλεία τοῦ Θεοῦ (Kingdom of God) to God's chosen people as promised in Isaiah. So you are mistaken in saying
Jesus is illustrating a particular person, not an entire Kingdom. In fact, he is referring to the βασιλεία τοῦ Θεοῦ (Kingdom of God) - his kingdom of which he has been coronated and abdicated rulership of by God. Instead of "illustrating" a particular person, Jesus is referring to a particular person: Himself, the prince, the delivering Messiah who is delivering and establishing the βασιλεία τοῦ Θεοῦ (Kingdom of God). So in this way, Matthew implies that Jesus was claiming to be King and royalty in the parables, but royalty of the βασιλεία τοῦ Θεοῦ (Kingdom of God) It is therefore appropriate to translate the text as kingdom of God, but to understand Jesus by inferance as royalty as the king of that kingdom