Some time spent surfing through the Mandelbrot set can be enlightening, as a more concrete example. Remember, no matter what you see in Fractint (or your choice of fractal generator), the K-complexity of the Mandelbrot set is very, very low. (Not quite as small as the Mandelbrot-generation process alone because you also need to describe the coloring algorithm, but that's not that much either.) But, to uniquely identify the image you are looking at to someone else, you must transmit not just the Mandelbrot generation routines, but also the coordinates you are looking at, or a description of the routine you used to get there. This can easily be larger than the rather small Mandelbrot algorithm. (It's easy to lose track of how deep you are in the M-set, without realizing that your computer is chugging away on computations involving thousands of significant digits...)
This is exponentially (super-exponentially?) more true to pick out a particular piece of a particular universe from a TM simulating all possible string theory universes. String theory may be simple (or may not be), by the time you're done identifying which of the 10^120 vacuum states you want to deal with (~400 bits right there), which initial conditions you want to deal with (no idea what that would take), and where in space and time you wish to point at (many thousands of bits minimum, no known upper limit), you can easily exceed the size of the part of the TM that describes the physics itself.
It might be helpful to try to forget everything you know about "complexity"; the English meaning of the word misleads your mathematical intuition. K-complexity is really something completely different (as is part of Elizier's point), and, frankly, it's much less useful than it seems at first blush. It's part of the wild world of Turing Machines, which can not be tamed or understood by any finite being. (And it doesn't really help that you can't prove if you have the optimal TM for a given result.)
It may also help to intuitively consider the difficulty of "pointing" at something, as in the essay. It is easy to gesticulate wildly at the Earth, from where you sit now. It is far, far harder to unambiguously specify which protozoan you are talking about right now. The part of the description that filters through the near-infinite possibilities to uniquely identify the topic of interest can be very, very large, and can easily exceed the size of the specification of "all possible topics of interest".