I think 'artificial' would be a better word here. For example, in Magic the Gathering, there is a very basic turn structure and set of rules that define the game (draw a card, play some cards, attack, play some more cards, done) that is convoluted by several factors, including an increasingly large dictionary of terms relating to abilities and powers of the cards, and a correspondingly dense set of rules to handle the inevitable complexity of all those things.
For example, creature cards have power and toughness. Simple enough. But then at some point, cards were printed that allowed you to modify those values. Now you have to mentally keep track of the actual state of the card. Then consider what happens when you have two effects like "add two to toughness" and "switch power and toughness" applied at the same time. Which one happens first? Much as in software, each new feature of the game inevitably has interactions with other features that have to be analyzed and handled appropriately.
Going back to the main point, this complexity is 'artificial' because it is not an emergent property of the rules themselves, but rather a consequence of the fact that so many rules have been piled on over time.
I'm not quite sure why the comparison is being made here at all. Go has an incredibly simple rule set and is a game played with perfect information. That such deep complexity emerges from those things is part of what makes the game so beautiful. In Magic, randomness and limited information are integral elements of the game, as are the myriad rules and their interactions. That "so many rules have been piled on over time" is not some sort of accident; it's been the intention from the beginning and it's a huge part of what makes the game fun. It's simply a completely different beast from a game like Go. Labeling one game's complexity "artificial" in some arbitrary manner is not meaningful. What's rather clear is that creating a rigorous mathematical model of Go is fairly straightforward, while doing the same for Magic would seem to be a few orders of magnitude more complex.
(Also, that a creature's power and toughness might change has been part of the game since the very beginning: see Giant Growth.)
I read "false complexity" as "complexity as imposed by a set of rules", as opposes to "complexity as an emergent behavior from very simple rules and interaction". Of course, adding any rule will add more complexity of the former, and probably the latter too. Whether one is more interesting than another is a matter of taste.
