There's more to a game than skills vs luck !
Indeed, randomness is a great part of a Mario Party game. That's what makes it interesting to play again in the first time. Like a board game that would relay on dices or cards. Random events are a big part of the game.
Does it makes it
all random though? No, because players have the power to react to these events, to make decision, and even to test their agility in mini-games. It's not only rolling dices until somebody win, it's handling events that can be in our favor or not. Shadow Hunters is close to that concept.
I know people though that are literally unable to enjoy anything else than dices and simple card games in term of board games. Anything more complex, and they're bored. Can't argue with tastes but, uuurgh, games where player actions never matter are as boring as, dunno, watching sports on TV.
But it isn't skills either! You're never good at Mario Party, you never train to be unbeatable in a mini-game (for a few exceptions). Not because it's only luck, but because these games are accessible enough that anyone able to press buttons and react quickly (or in rhythm) can success! You don't win because you're trained, or because you got lucky… You win because this time you played well, or because you've tricked your opponent(s), or they have been distracted, etc… It's still arcade, with a but part of random, but where player actions matter a lot.
It's almost comparable to Mario Kart, in a casual context. Sure, there are talented players and competition in these one, but there's also a large part of the public that isn't particularly skilled. And (unfortunately

), I'm definitely in this second one. But Mario Kart is a game cleverly designed in order to make everyone have fun. With players around my level (which actually mean a lot, including even good players), I sometimes lose and sometimes win according to the circumstances. And while objects are a big part of the game, it would be lying to say that only luck mattered. But is it's skill? No. When nobody play perceptibly better than anyone else, the victory depends on the performances of each other.
That's what defines good party-games: games where everyone is naturally good. Not because it's only based on luck, but because it rely on rules that everyone understand immediately, capacity that everyone has, and strategies that can be creative (you can make mistakes and smart moves in MP, but there's not really any winning strat). It's games about the instant.
And thus they are indeed very different from competition games like Street Fighter or even Smash Bros. Those really are games about skills, and get richer and richer the more we train on them! But party-game aren't about skills. There is no skills indeed in Mario Party, and you don't win by being stronger or smarter. It's mostly interactions between the players, and that's what matters the more!
Sure, luck always play a part, like a lot of multiplayer games. But great casual and party games are those that, while putting every player on the same level, make their actions always relevant.