Here's some thoughts. Don't know whether they're necessarily correct, of course.
I suspect there would be more options for trading between coins, buys, and actions. As it is, keeping in your head how many actions, coins, buys you have isn't that hard, but I can understand why there aren't any plans for cards that mess with that - Diadem gives you coins for your spare actions, but that's it. If it were designed from the start as a computer game, it would be a lot easier to deal with tradeoffs - if there's big public counters for [coins, actions, buys] then it's no big deal to have cards that have minuses as well as pluses. It's a design space which is easier to deal with when there's an automated counter.
Card complexity would have an additional factor - number of clicks. I suspect cards would be made to minimize tedious clicks. As it is, Hamlet-Library is SO ANNOYING to play with or play against online, in a way that IRL games don't have. I bet that Hamlet would work differently. Going along with that, I would GUESS that for attacks with choices, you'd make the choice before seeing a reaction, at the same time as you play a card. (Again, to minimize clicks for obvious choices. Your Pirate Ship card would have a nice graphical interface - you play it by clicking 'Attack!' or 'Coins!', single click to play the card, without reactions. In a long Minion chain, it would take one click per Minion instead of two. But if there ARE reactions, you obviously can't change the interface for just those. In person, there's no need - without reactions, you just say 'Pirate Ship, Coins' immediately, but online that involves an extra click.) Obviously, there may be rebalancing that goes along with that. It's not necessarily better, just more suited to online play IMO.
Durations that last longer than one turn, or variable numbers of turns. IRL - you're not going to expect people to remember exactly what they played two turns ago.
More actions that give plusses based on what the opponent did on the previous turn. '+1 action for every 5 action cards your opponent played last turn, rounded up. +1 card for every attack card your opponent played last turn.' Or stuff like that. Obviously you can do things with treasures, vp, actions, etc. Not so feasible IRL because cards get discarded and you don't remember exactly what happened - Smugglers is about as much as you can do with that IRL, you can't get too complex.
You would probably only be able to reveal each reaction once per attack. As it is, the reason you can reveal more is I think(if I remember Donald's comments correctly) partially due to accountability - you can't know whether the other person has one Secret Chamber in hand or two, or if they drew another one from the top of their deck, or so on. Same with the others, you don't know whether it's one reaction multiple times or different ones. Electronic accountability makes that easy.
In general, any design decisions that were made for the accountability reasons would no longer need that.
Oh, and there would be awesome animations for everything.
most cards could have built in logic that autoplays the card
Disagree. The game is complex enough so that card plays are very rarely automatic - controlling reshuffles and all that, I don't *always* want to play that Smithy or Village if I know what's left in my deck.