Go is more complex that Dominion. Starcraft too (as AI can still only just crack the top 99.8 of players) But Go is (was) known as the most complex game in the world with the most possible changes in strategies and permutations. However, due to its RIDICULOUSLY intricate set of rules Magic The gathering has recently passed Go as the most complex game in the world.
I think you -- and perhaps also the article -- are conflating several concepts, here.
The Magic result shows that the game is uncomputable. That is, it proves that there are circumstances in which you can show a computer two potential states of a Magic game and it will be not just unlikely, not just very hard, but
impossible for the computer to say whether or not state B can be reached from state A.
This was achieved by embedding a Turing machine in a game of Magic, because that's the thought-experiment machine Alan Turing constructed to prove the Halting Problem cannot be solved in all cases.
Go and Chess are
not uncomputable in this rigorous sense. There are fewer than 20,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 possible positions in Go, so a computer can work through them all one by one. Maybe not before the end of the universe, but that's beside the point.
That's a cute, possibly even important, theoretical result. But it says nothing about how any real-world game of Magic would ever play out.
The complexity of a game's rules are a separate consideration. Here, it's pretty clear in an intuitive, human, sense that Go is simpler than Chess, is simpler than Dominion, is simpler than Magic. The rules of Go fit in a couple of paragraphs, whereas the Magic rulebook is 250 pages. Edward Lasker once said "While the Baroque rules of Chess could only have been created by humans, the rules of Go are so elegant, organic, and rigorously logical that if intelligent life forms exist elsewhere in the universe, they almost certainly play Go."
A third question is how competitive computers are against human players. We know that computers now reliably beat humans at Go and Chess. We also know that machine learning can figure out how to beat humans at Go and Chess. We know computers aren't beating humans at Dominion yet; I don't personally know how good computers are at playing Magic right now. On the other hand, I'm not sure having computers beat humans at Dominion has received anything like as much research attention or computer power as the iconic problems of beating a human at Go or Chess. My intuitive sense, as a player mainly of Dominion and Chess but not Magic or Go, is that Dominion is a lighter, easier, less mind-bendingly cerebral game.
