I think people are vastly underestimating (or rather, perhaps not estimating at all and "bypassing") the number of "calculator friendly" handicaps available to a hypothetical Dominion AI. Stuff that it's just better to have a machine do. The machine makes railroad better than John Henry because it runs on coal.
In Jeopardy, the advantage was buzzer pressing, for the demo they let the AI get the full advantage of seeing the permission light and reacting in .0001 seconds instead of the standard 0.7 seconds and always got first crack at a question so it could answer lots of questions wrong and still win. In Starcraft, there was infinite micro, which would be the second greatest benefit that I'm aware of, the ability to spend essentially no time telling an individual unit to do something different from its peers. Starcraft was a balance between exploiting that advantage and having a similar "god there's so many things for your grade school teacher to cover" dimension similar to Dominion.
In an FPS with reduced character size it'd be so trivial to exploit those kinds of advantages that people don't write AIs to do it because it's too boring and easy. The handicap is too huge. That's assuming the design of the FPS is such that expert players miss a little bit or have to slow down to take their shots, of course, but with very much of either it becomes so huge.
Chess's AI friendly task is checkmate puzzle solving. But the way chess works, the really hard part happens before that even comes up, one player generates strong advantage before mating puzzles start to really be presented. So mostly chess was a matter of making the AI smart enough to win, with no calculator based advantages at all. I don't know go well but I expect it's a pretty similar story. I think it's possibly kind of true that the amount of time the AI had to not lose before it could start checkmate-puzzling off of information advantages is more generous in chess than in go, that is possibly the meaningful way of looking at it. It could just be that Go midgames are flat out harder, though.
What Dominion is gonna have is greening phase and I think that should be appreciated. The decision to start buying provinces, or to buy a final gold knowing exactly how many times you'll draw it if you really sit down and think about it, the exact probabilities involved in Duchy dancing (with perfect deck tracking. I'm sure our highest tier players have a vague idea of what's likely soon towards the end of a dominion game, but don't think they can recite their opponent's remaining 8 cards before next reshuffle and their own consistently. And it's almost totally about knowing what the next hands look like and not any of the big brain strategy of needing just one village mixed in with Ironmonger on X board because an expert intuits which drawing terminals are going to be the right purchases at the right time when hitting 5 - it's just stuff like "yeah if you actually counted up every single card, there's only a 87% chance your opponent can end Duchy dance prematurely not 92%, therefore you -should- actually buy that spice merchant and expect to nuts topdeck it for a province-duchy turn, or whatever, stuff like that.
And those kinds of advantages are going to be pretty big in a probablistic game where the players should be expected to trade wins anyway, even just off brutish data gluttony on the timings of village genus cards and smithy genus cards and woodcutter genus cards at certain times on certain boards from reading tons of logs.
So, my expectation is, using that handicap, beating every single human should be -easier- than go (i don't want to say chess) because a significant subsidy exists, and the difficulty in memory based card counting + essentially discovering new game specific texas-hold-em odds for endgames exists. It's still a jillions and jillions of dollars thing though.
tl;dr if you are up a knight in chess I don't think you need a ti84 to checkmate without throwing away your win 15% of the time, if you played more correctly enough to have a similar strength deck to your opponent but with a 5$ where he has a 4$ there's a brutish way even a ti 84 would give you an appreciable winrate bump, and I think that could be considered. It overrides the subtle difference between what ironworks and smugglers truly mean I would think. I could see how you might think there are just so many cards that can be classified in so many ways that maybe it would take forever and ever to program the AI to where it's never hardthrowing entire games over things like, "Oh, this board has transmute on it and that's a way to gain action cards, so the principle that Graverobber generally counts as a +buy has force in this kingdom". But I think with the millions of dollars and as many people working on it as worked on chess, you eventually knock every single one of those bowling pins over, then you get into the range where the computer is like 5% worse than Stef and largely mirroring him, but doing perfect deck tracking stuff on the ends of games and winning 17 game series consistently.