He knocked up the Queen right after arriving in that world, he had already set the stage to take over that country MONTHS ago
Well it was also part of his Deal with the Queen, isn't it.
The King created the Empire by having every country under him and becoming the Emperor. But because of MC's plan, he lost his position allowing the Queen to become the Ruler, aka., the Empress of the World, which was the 2nd wish of the Queen.
As for knocking-up the Queen, that falls under both the 2nd and 3rd wish of the Queen.
By getting knocked-up and claiming the child to be that of the Emperor's, the Queen has legitimate reason to rule the Empire as long as she wishes, even until her death if she plays her cards right with the upbringing of her child (solidifying her 2nd wish).
And her 3rd wish was to belong to MC both in mind and body, and what better proof of that than getting knocked-up with MC's child.