The other person has to wait while you play your cards. It is then polite to return the courtesy and let the other person play their cards.
No, it's not polite to make them play their cards when there's no point in doing so. If you think clicking on cards on Goko is fun, then you can play against the bots or whatever; I assume that most people would rather be doing something of significance, such as playing another game of Dominion against someone who hasn't decided to resign yet.
Everyone prefers their own turn to the other guy's turn. Almost all of the resignations I encounter come around the beginning of my turn, because the other guy played his own cards, because it was a little fun for him, and then resigned, because waiting through my turn was not at all fun for him.
If your opponent is playing a turn you think they would rather not play, if they knew you were just going to resign, you can tell them that, and ask if they mind if you resign. "But wait! That means going the extra mile just to avoid offending someone else! I mean, there's a chance they might not have even minded if I just resigned!"
Well, that's what it means to be polite. Going that extra mile.