For the benefit of causal forum readers and the semi-literate, this is the kingdom:
This is only an okay Rebuild board. The engine is respectable, there's no strong $3-$4 terminal, and there's no cantrip sifting or game-breaking Rebuild combo. That said, it's still a game with Estates and no Colonies, and the's engine isn't all that fast. As usual, my money's on Rebuild.
Mic Q makes a good point about Minion keeping you from getting to $5 in the late game, but that's not what cost you the win. Your mistake was following the advice in my article. That is, following advice and strategy for a Rebuild mirror rather than a Rebuild-vs-Engine race. In the mirror you grab Duchies early because Rebuild isn't much use without them. In Rebuild-vs-Engine you pile-drive Rebuilds and try to run out the Provinces before the engine can catch up.
Because Duchies aren't going to run out, you don't need to make early sacrifices to secure your share. Buy a third and a fourth Rebuild without hesitation, rebuild into 3-5 Provinces and then start trashing the rest by rebuilding Provinces into Provinces. A fully-functional engine is going to gain VP way faster than Rebuild, so ending the game before that happens is your #1 priority.
I'm only annotating your most important turns:
T1: Hamlet is almost a null card for Rebuild, which doesn't need the actions and isn't likely to use the buys. Better to spend your $3 on a Silver or a Steward.
T2: Baron isn't very good in the non-mirror and it's never all that great as a T1/T2 Rebuild buy. You can't make much use of an early $7 hand, and you don't want a pile of Estates any time soon. Baron can miss and leave you with $4 on T3 or T4 and it's almost certain to "miss" later because you'll be emptying your deck of Estates.
T6: Definitely buy a third Rebuild instead of this Duchy.
T8: With Steward + $3 in hand, just use the Steward as a Silver and buy another Rebuild. Drawing may be useful later for cycling, but right now it's not worth the risk of failing to hit $5.
T9: Again, buy Rebuild instead. This Duchy might make sense on T9 of a mirror, when there's only 1-3 Duchies left, but here your focus is on rebuilding into Provinces and then trashing the remaining Provinces.
T10: Note that this is only the second Rebuild you've played this game. So far it looks more like you're playing something like a Duchy/Hamlet rush. That's not a strategy that really puts a Minion engine to the test.
Note also that yudai214 is up to 8 Minions. Regardless of how many Estates you have left, it's time to start gaining and even trashing Provinces instead of rebuilding your Estates. Name Estate and rebuild Duchies or trash Provinces from here on out.
T12: Again, better to rebuild a Duchy than an Estate.
I'll stop commenting here. You're now facing 10 Minions with only 2 Rebuilds and all 8 Provinces still on the table. There's no real chance of catching up.