If your game is as messy as JThorne described, you are misplaying it.
This may be a shocker, but I actually agree here, with a small caveat.
If I'm interpreting correctly, this statement is basically saying this: If you're buying village/smithy pairs, and a terminal coin/+buy card, then you're playing an engine. If you're only buying one Province a turn, then you are unequivocally doing it wrong. Either you should keep building until you can reliably draw deck and get to $16, OR you should NOT have been trying to draw deck in the first place and should just play a BM game. In BM, Villages are almost always do-nothing cards that might as well be Pearl Divers without the topdeck.
If you're playing a BM opponent and they start buying Provinces first, if you get nervous and stop building and start singling Provinces, you're also doing it wrong and you have lost. If you stick it out and build for doubles and you still lose, then you chose the wrong strategy for the kingdom in the beginning. I totally get it. I've been both on the winning and losing side of this situation. Mostly winning.
That's not to say I haven't played a single-province engine. In a kingdom with no buys and no gains, and especially with decent trashing, there are times when money and sifting can create an incredibly reliable engine that's more reliable than BM even if it's just singling, but that should be the plan from the beginning, not something you settle for when you realize you made a mistake.
Anyway, the caveat, and it's going to make Awaclus roll his eyes.
Multi-player.
The best laid plans can go radically awry depending on what other players do, or if just one of a few opponents gets a lucky draw and grabs too many of a key card early. You may have to bail halfway through engine-building. In my experience, the most effective way to victory in multi-player is one of two things: 1. Figure out if there's an engine that can run on no more than 5 copies of any one card. 2. Pile control.
4-player games almost always pile out, but I've certainly played deck-drawing engines that started doubling before piles emptied, forcing other players to play catch up (Thanks Donate! You're the best!) 3-player games give you more ingredients, and if one player ignores a key card, you can play that strategy like a 2-player game.
But you have to keep your mind open to many possibilities. I just won a game where I had one opponent playing BM, one playing a Hireling engine (no, no, no a thousand times, no) and I won what basically amounted to an extremely weird rush. Procession/Lurker, with both Museum and Obelisk in play, and Lurker was the Obelisk card. You can guess how that went. One opponent was Processing Lurkers in order gain Hirelings. I was Processing Lurkers...in order to gain their lurkers from the trash. (And processing into $3 Chariot races, Processing them into more Processions, then into one of each $5...)
In a kingdom with no decent draw, no trashing, and no +buy, I emptied piles with a final massive Lurker party, bought the last lurker, and landmarked my way to a victory over opponents with several provinces each (I bought one for the 8VP, because that's hard to pass up. That and the 5VP Duchy.)
Also, another weird game: No +buy, no +actions, lots of terminals. I don't remember the rest of the Kingdom, but here's what I did: Banquet Catacombs, Transmogrify. Silver, Banquet two more Catacombs. On the first Catacombs play, buy a Gold. On the second, Donate all starting cards and take only one debt. Next, Transmogrify the Catacombs into a Gold and another T-Mog, buy a Province. Mat the T-Mogs. Start milling Province/buying Province. At some point I think I did a T-Mog a Catacombs into Gold/Remodel late for a Remodel Gold to Province ending. It was ridiculous fast. Game was over in close to ten turns, and I ended up with six Provinces (out of 12.)
So, what's that? I only bought one Province at a time. It's definitely not an engine, because I never actually drew deck, but I could sure line up $8 with Catacombs pretty easily in a deck with that few cards. From my perspective, that seems like a BM strategy, but it certainly underscores the fact that BM isn't simply "buy money and a couple of terminal draw cards and then points."