It certainly seems to be that way in code, anyway.
If you throw a bunch of carbon, oxygen, and other organic compounds into a vat, you're vastly less likely to get a fully formed human being than, well, a disorganized pile of matter. Usually you wouldn't consider the random clump of molecules more complex -- there are practically an infinite number ways to rearrange a pile into a pile. In contrast, there are many orders of magnitude fewer ways for a human being to emerge.
That said, there is a sense in which the random pile of molecules is more complex. If I want to predict the motion of every (or at least, most) of the molecules in that vat, it's easier to predict the bulk motion of a human than each molecule moving per the Maxwell–Boltzmann distribution.
Similarly, it's easier to compress a static black image than continuous random noise. Notice that a static black image is more organized, more easily compressed, and less likely to occur by random chance (assuming noise is the default). Therefore, a static black image has less entropy. Whether you want to call this state more or less complex is a matter of definition.
However, the article is stating that this is not an accurate view of the mathematics - and that a more accurate view merely requires more disorganized distribution of energy, while matter may be arbitrarily better organized and still have its entropy increase. For example, crystalization of a material does not necessarily decrease its entropy, as long as the crystal formation dissipates heat.
It's tempting to simplify the universe like any other system: one for which microstate descriptions will have a fixed number of microstates across which the available energy will eventually be distributed more or less evenly. But perhaps that's a bad simplification. The article says as much, but in the middle of a bunch of claims about order and disorder.
So what's confusing about the article is it's attempt to describe the... confusion, that the new interpretation leads us away from.