Even with the RNG bullshit in Mario Party, it's not exactly that surprising why Dan wins most of the time. Considering that Dan wins most of the mini games on average, that means that he almost always has a decent amount of coins. This means fewer times where he shows up at the star without enough coins and also it means he can buy more items. And this is helpful since Dan actually uses his items a lot and doesn't horde them.
Add on top of this the Bonus Star at the end and also the fact that Dan generally pays more attention to the game than the rest of them and it's pretty easy to see why this happens so often.
I will say that this map seemed to have less bullshit than most of the others ones they have played so at least most of the game was pretty competitive (which makes it more entertaining to watch).