Mario Party isn't exactly a conventional board game.
My theory on how this will work is that you'll roll the dice, land on a square, and something will change about your character - you might get some stat boosts, get an item you can take into the next battle, perhaps get to play a challenge room for a chance at bigger prizes, or even lose some stats or take some kind of penalty for the next challenge. Then once everyone has rolled, there'll be some kind of showdown between the players where the winner gets points / more boosts / some other kind of victory thing.
The game either wins when someone wins enough challenges, or when the turns are up there's some kind of super climactic final showdown to take the whole thing. Something like that.