One interesting topic to come up in Goko-related discussions (on BGG mainly, not here) is asynchronous play. The usual answer is "it wouldn't work", which is of course correct with the current rules, because Minion-Moat-type games would be a nightmare. But maybe varying the rules could make async play work.
I think that async play ideally wants each player's turn to require no decisions from his opponent. You could ask for more maybe, like being able to specify multiple turns at once (especially in the opening), but this is good for a start.
So, I made a list of cards that currently have a player make a decision when it's not their turn. These fall into two categories: reactions and opponent-choice. First the list, then a discussion of how they might be changed.
Reactions
Base: Moat
Intrigue: Secret Chamber
Prosperity: Watchtower
Cornucopia: Horse Traders
Hinterlands: Fool's Gold, Trader, Tunnel
Opponent Choice
Base: Bureaucrat, Militia
Intrigue: Masquerade, Saboteur, Torturer
Seaside: Ghost Ship
Prosperity: Contraband, Mountebank, Rabble, Vault, Goons
Cornucopia: Tournament, Young Witch, Followers
Hinterlands: Duchess, Oracle, Margrave
Promo: Envoy, Governor
Overview of Discussion
There are two main ways to adapt cards: one is to make the decision automatic, and the other is to delay the decision to the beginning of next turn. Making a decision automatic loses some flexibility compared to the current rules, but otherwise is faithful.
Delaying the decision can make a pretty big difference compared to current rules, although it often gets played this way IRL in situations where it doesn't matter. Sometimes it matters a lot, e.g. playing a discard attack to help your Tournaments, which is an interaction that would be lost.
If you're playing asynchronously online, the server could choose to report delayed effects one-by-one, to help preserve the frustration of not knowing how many times you'll get hit by Torturer.
Discussion of Reactions
Moat and Horse Traders are easy: just force them to always be revealed to attacks. Although you don't always want to do this, usually you do. IRL, it's difficult to make this accountable (because your opponent can't tell the difference between you failing to reveal Moat and simply not having one in hand), but that's not a problem on a computer.
Fool's Gold's reaction is fine to delay.
Secret Chamber, Watchtower, and Trader are difficult to deal with. Trader could perhaps be auto-revealed to anything your opponent gives you, because almost never will they give you something better than a Silver. Watchtower is tough, because sometimes you really want to trash (Curse, Copper) and sometimes you really want to top-deck (Silver from Governor or from revealed Trader)--maybe it's best to delay the decision, so that in the meantime, the card is set aside. Secret Chamber seems almost impossible to adapt, because delaying the decision would make it useless against deck attacks, so the card would need a redesign.
Tunnel is obvious. Reveal it always. Has anybody ever not revealed Tunnel when they can? There are some problems with accountability here again, since in principle you can discard in a way that hides the Tunnel from your opponent.
An example of an interesting card interaction lost by these changes: not revealing Moat to a Mountebank so that you can reveal Trader instead.
Discussion of Opponent Choice
Some of these are no-brainers: for Tournament and Young Witch, auto-reveal always. Like with reactions, there would be accountability problems IRL. Mountebank is less clear-cut, but it's usually good to reveal against it, so auto-reveal for that card too.
Oracle and Rabble sometimes require re-ordering cards that go on your deck, but it rarely matters, so they could be put back in original order. (Remember that the reason re-ordering is usually allowed is that, IRL, it's hard to keep track of the original order. This isn't a problem on a computer.)
Discarding and put-back-on-deck effects (Bureaucrat, Militia, Torturer, Ghost Ship, Goons, Followers, Margrave, maybe Vault) can be delayed.
(Then there's a question of whether opponent-draws-a-card effects should also be moved to the beginning of opponent turn. I think they should, because the interaction of opponent-draws-a-card effects and discard attacks is important pretty often.)
Saboteur's gain, Governor's opponent-remodel, and Duchess's self-spy can all be delayed. For Governor and Saboteur, your opponent should get to resolve these effects even if the game end condition is fulfilled before their turn starts. (Note that moving Governor's effect can hurt a lot if you are defensively remodeling $7's into Provinces, so this loses some interesting situations.)
Masquerade, Contraband, and Envoy all seem impossible to adapt. With Masquerade, the pass could be removed, which makes the card much less interesting but at least preserves part of it. I don't see any way to deal with Contraband and Envoy.
Conclusion
Using the changes suggested above, nearly every card can be adapted somewhat reasonably to asynchronous play, with the loss of some interesting interactions. The exceptions are Masquerade, which needs its pass removed, and Contraband, Envoy, and Secret Chamber, which seem impossible to adapt.
Compiling this list made me realize how much worse Dominion would be without interaction on opponent turns. Sure, in most games it doesn't make any difference, but the games where it does matter are some of the most interesting games.
That said, the core of Dominion would still be there. It'd still be a fun game, albeit a little less so than normal.