Uh, what, exactly, would stop a future computer from performing at just as well as a human at any of the bottom items?
Calvinball is completely impossible, because the primary skill required is creative thought. Most humans are not creative enough to play it well. Calvinball is also a particularly unusual case, because the rules are not fixed.
Mao also doesn't have fixed rules per se, but they only change accidentally, after the manner of the message in the telephone game. The players don't change the rules during the course of one game of Mao, and only the player who is teaching the game to the others could even potentially change them. I suspect that if an interface could be worked out to allow humans to play Mao with one another via the internet, a computer player could probably be constructed that could hold its own. It would be an interesting programming exercise, but I can't think of any reason it couldn't be done. The "learning" that the game requires is essentially just memorization. Computers are terribly bad at certain other kinds of learning, but they can handle memorization just fine (better than humans, I daresay), if you program them to do so.
Incidentally, I once adapted the basic principle of Calvinball into a card game. A group of us played it two or three times. It worked surprisingly well. There's absolutely no way a computer could have been programmed to even participate, much less to win.
If I'm not mistaken, Snakes and ladders has no strategy.
That would be my assessment as well.
The other games would be satisfied by any system that satisfactorily passes the Turing test
The general-case Turing test is generally assumed to be AI Complete. I don't know whether this has been satisfactorily proven, but I'm certain it hasn't been disproven.
and as far as I know, there's no reason to think a future system couldn't at least PASS as human
In limited cases, it's already been done -- but only in limited cases. The computer can pass as a particularly unintelligent human (e.g., mentally retarded child) or as a human that the "judges" wouldn't be able to interact with in any meaningful way (e.g., a human who doesn't know any language the "judges" know) or as an uncooperative human who refuses to play the game straight (provided the competing human is similarly deficient). The computer can also pass if the "judges" are remarkably bad at what they're doing.
But if the judges play the game straight (try to carry on an actual conversation) and the human participants are regular people off the street, the whole thing doesn't take very long. Computers fundamentally aren't smart enough to participate in a normal human conversation, because they don't understand any of what's being said. It becomes obvious rather quickly.
Actually, such an AI might just outperform in Mao and Calvinball using perfect, faster recall and procedural rule generation.
Mao, yes. Calvinball is impossible. Perfect, faster recall doesn't help AT ALL in Calvinball, because the whole point is to AVOID being bound by your opponent's rules, by strategically creating rules that favor you. Any kind of "procedural rule generation" that a computer can be programmed to do is going to fall flat on its face against a moderately clever human player. Furthermore, no strategy can be pre-programmed, because all the strategy is in what rules you make, and the only permanent rule is that you can't make the same rules twice. Pre-programmed strategy of any sort could only be used once, ever. Calvinball is quite possibly the pathologically worst possible game for AI.
Games that have a lot more strategy than tactics are almost as bad. If you study a lot of game AI, you'll notice something: in games that play to a computer's strengths (chess, blackjack, Scrabble, hangman), the AI consistently has to be programmed with difficulty levels, so that if you set it to easier it can back off a little and let the humans feel like they can compete. Because otherwise, the humans can't compete. In games that are complex and have a lot of long-term strategy (e.g., the Civilization series), the AI has to be programmed to "cheat" (i.e., to have advantages the human players aren't permitted, like always being able to see what their opponents are doing even though the humans can only see within a certain radius of their own units) and still presents only a moderate challenge to human players -- playing against a human in such games is MUCH more difficult than playing against the AI. Granted, the AI for these games is seldom as good as it theoretically could be. But even if the world's top AI researchers poured decades into the problem, the computer would never be able to compete effectively against an even moderately skilled human player.
(On the other end of the scale, the best games for AI are probably ones that involve a combination of rapid memorization and the ability to act quickly. Dutch Blitz springs to mind immediately. If there were a non-turn-based "Speed Scrabble", where you can play as fast as you can come up with plays, it would take me about five minutes to program an AI no human player could ever touch.)