The king in the portrait of sin sukju is portrayed with a lack of background because

In art, lack of background in potrait painting is usually done in order to capture's the viewer's attention solely on the person in the potrait in order to appeal to the person's positive traits (whether its their beauty, charisma, or expression)
A full background will tend to divert viewer's attention from this.

The king in the portrait of sin sukju is portrayed with a lack of background to focus on the merit of the subject. This allows the subject to be the main focus of the portrait and not give anything away to the background. The portrait is typical of the Korean court artist.