While it is possible that Sadoko usurped the king of Nod/Dreamland/Pop Star*'s power**, it is also possible that the swirly eye effect is common among all Dreamers visiting Nod***. Whether she did steal the powers of the king or not, however, it seems to be a general consensus that Sadako pulled a Macbeth.
It seems that this plot detail is soon to be worked out.
-B.O.R.K.
*(Kirby reference. Had to do it. Every time I hear the word Dreamland, I am reminded of Kirby. <('.'<) )
**(Some have noticed that the king's swirly eye and Sadako's swirly eye are on opposing sides, meaning that if they look at each other, the swirls would be looking into eachother. Make of that what you will.)
***(Some have noticed that, when a dreamer other than Sadako uses Dream Warping Powers, their hair tends to subtly cover one of their eyes. I love how the author works such minute yet important details into her work: Sort of like the difference between British horror movies and American 'horror' movies.)