So, the entire article as currently constituted is based on two-player games. Things change big-time with more players. I'm not an expert, but there's some light I can shed.
First of all, duchy/duke tends to be a lot weaker in these situations. That's something to get out of the way right off the bat. The big reason for this is goes back to one of the first things I say in the article, that the game is a lot longer in non-mirrors, because you've got one person going for provinces, the other going for colonies, and so neither end condition gets met very soon. That's sorta true in multiplayer too, but not nearly as much. Province player doesn't need to get all 8 by himself anymore.
Ok, so looking at 3 player, if we've got 2 players going province and 1 duchy/duke, we get that we'd expect 6 provinces each for the province player, which hey, that's fewer points. So you only need 6 duchies and 3 dukes to overtake that. Unfortunately, most pretty bland, standard decks can get to 6 provinces without that much trouble, and barely need to change their basic game plan to beef up. Also, it's very likely you'll get a 7/5 split on the provinces, and you need to overcome that 7 to win. So you end up often needing almost just as many duchy/dukes as in 2-player, but you've got less time. Anyway, still possible with support (you need support now though), but green a touch sooner and duke>duchy a little sooner.
If you have 2 players going for duchy/duke, then province player getting even a single duchy is a pretty big deal. He also has access to a lot more provinces overall. And because there are only 12 duchies for the 2 players, they're going to be stunted a bit more. So this looks really good for province player on most boards.
There are a couple of boons with 3-player to the duchy/duke player, though they generally aren't enough to make up the deficit. Namely, other piles are going to run out faster. So if duchy/duke can get a lead, the game's going to end sooner, and province doesn't have as much time to catch up. Also if the two province players get slowed down dancing with each other, you get time to catch up. And finally, lots of those single-card engines where you need a lot, your opponent can't get so many. So you're less likely to get pummeled by a player with a huge minion or HP or conspirator engine, 'cause they can't get as many.
4-player makes things even crazier. So, everything from above gets even further compounded. Your opponents have 4 provinces each, which isn't that much at all. You should flip to buying dukes after like 5 duchies probably. Certainly not more than 6. The game's going to be so short, you might actually hold up ok, if you can get a quick 3-pile; it's not SO rare for racing to duchies to be good in 4-player anyway. But likely, in 4-player, the game is so short that you really really need to listen to your shuffle luck. By that I mean, if you're getting 6s early, go for gold and provinces. But if you get 5s, then roll with the duchy/duke. Okay, more complicated than that, but the idea is to have a strategy flexible to whatever you draw.
That's about all I got.