you saw monty use horse archers to defeat an industrial age empire......
O RLY!?
He also mentioned cavalry...
I've seen a mix of knights/cavalry slam into infantry/SAM infantry and capture multiple cities. I've actually seen Monty do this as my VASSAL (I have a game on this forum where it occurred).
I've done it myself with grenadiers + cannons too. Infantry can only hold out so long if it's a 5 city empire vs a 20 city empire and the latter is managed well for hammers.
Remember, inherently a mounted unit like a knight with 2 promos is pretty strong. It will ignore the rifle's drill, although the rifle gets +25% against it. Odds are, with first strike immunity the knight will damage the rifle significantly. A 2nd knight will actually have the odds on the same damaged rifle. In other words, 8 knights will generally beat something like 3 rifles, especially after collateral damage affects the latter at least somewhat.
Another note: A CR III mace will actually beat an unpromoted rifle defending a city with no culture defense

. That's pretty scary, but it gives you an idea of what a dangerous, troop-spamming warmonger is capable of if he gets momentum and GGs. I've seen Monty win some early wars, settle the GGs, and start pushing out tons of combat III knights. When you're talking 50+ stack sizes, that type of unit is incredibly dangerous. Of course, I've done similar things myself (just as recently as today

), to great effect. A tech lead is great, but so is having things like CR III trebs, combat IV knights, etc. The latter can ALSO cut through medieval troops with minimal losses and will generally destroy opposition at tech parity with ease. A promotion lead is almost as powerful as a tech lead, but usually easier to achieve!
So when those knights become cavalry, and you see combat III or pinch promos on those cavalry, just how far behind infantry do you think they are in effective strength? They're behind, but not by enough that 1 infantry can beat 2 cavalry.