Dominion would indeed work with webcam, because everyone only shuffles their own cards, but you can only play with the cards that everyone has (if one player has an expansion and the others don't, you can't use it).
If all of your players already know how to play, I strongly recommend the official Dominion Online [0]! The base game is free, and the expansions are very affordable too ($1.95 for a month with half the expansions [the older ones], or $3.90 for all, no recurring charges, and only one player at the table needs to have bought them). Unfortunately it's not very intuitive as an introduction to the game because you don't get a good feel of where cards are coming from and going to, but once you know the game it's arguably better (because of the instant setup and shuffling, and automatic tracking of effects).
If all of your players already know how to play, I strongly recommend the official Dominion Online [0]! The base game is free, and the expansions are very affordable too ($1.95 for a month with half the expansions [the older ones], or $3.90 for all, no recurring charges, and only one player at the table needs to have bought them). Unfortunately it's not very intuitive as an introduction to the game because you don't get a good feel of where cards are coming from and going to, but once you know the game it's arguably better (because of the instant setup and shuffling, and automatic tracking of effects).
[0] https://dominion.games/