1980s new wavers named after twins, when there were three (?) imagine themselves as benevolent sovereigns.
A king (or it could be the queen, even a pharoah) is the head of a state/country, in this esteemed position based on birthright. One would be king for life, not for a day, unlike this song’s request.
In modern times the monarchy performs a largely symbolic and ceremonial function. So, perhaps the Thompson Twins are referencing the earlier days of such sovereigns, then widely seen as dictatorial, possessing near absolute power over their kingdoms and empires. The Magna Carta (Great Charter), in 1215, started a long process of limiting the power of kings, putting a document over them, a constitution.