I would just like to mention that there isn't really any reason why this shouldn't work on PC. The only problem is the way in which you engage other players. I think that, instead of following the typical Nintendo approach (which is sadly not really practical for an Indie making multiplayer games) you should experiment with something more along the lines of a way for a community of people to engage in competition against each other.
Mario Party is essentially made by it's minigames, not the board itself. As 
sqiddster said, "Those are usually just a huge collection of minigames held together by some meta." that statement in itself is important in the context of a party game. Considering this, I think that a game that used the the User Media plugin and brought a number of people to compete against each other in a series of quick mini games would be fun. You could hold the stats of the player locally and just have them compete in a series of mini-games against random online players, on camera. It'd also strongly encourage let's plays, which would do a lot for marketting the game. As long as it's well made, I really think it could work.
Also, just a side note, if you were to go this route, it'd probably be best to publish it to a social network, like Facebook. I don't know if anybody actually plays games on Facebook anymore, though.