First off, the image comes from William Thackeray's The Paris Sketch Book, which was published in 1840. Thus it was not only produced over a century after the Sun King's death, but also by an infamous English gadfly. In terms of both audience and context, the cartoon would have been quite different than contemporary French satires of Louis XIV in the seventeenth and eighteenth centuries. The cartoon itself is on p. 435 of the link, and the text provides some idea of what Thackeray was satirizing. The King, he notes was a "little, lean, shriveled, paunchy old man," and there "is no majesty in him, at any rate," [emphasis original]. But as the cartoon visualizes and the accompanying text makes abundantly clear, the excess of laces, wigs, and other frippery elevated such a shriveled old man to something majestic. Yet, Thackeray notes that despite the obvious falsity of his image, many buy into it:

Thus do barbers and cobblers make the gods we worship: for we do not worship him? Yes; though we all know him to be stupid heartless, short, of doubtful personal courage. worship and admire him we must; and have set up, in our hearts, a grand image of him, endowed with wit, magnanimity, and enormous historical stature.

The Paris Sketch Book is not satirizing a cult of Louis XIV, but rather how many of the author's contemporaries had a superficial understanding of the men of the past based upon their own superficial self-presentations. Thackeray goes on at length as to how the historical Louis XIV was at odds with this image, but that many Europeans simply pretend as if paintings like this famous portrait or Bernini's equestrian statue were the reality of the Sun King's rule, not an expression of his vanities or politics. By visualizing the King as a paunchy, little man dressed up as something grand, Thackeray lampoons such a shallow view of the past.