Non-terminal draw is a relatively simple concept: Handsize-increasers you can easily spam without needing villages. Based on their positions on the Qvist rankings, though, they actually seem to be some of the cards I least understand. Things that confuse me:
Laboratory - Lab gets trashed a lot. The main reason given is that "the draw is weak." Well, yes, it only increases your handsize by 1, but the fact that it combines drawing and non-terminality into a single card is huge. It seems to me that people are underestimating the number of Lab boards where there's either no villages or no terminal draw. In either of those cases Lab is a crucial card.
Even if there are both villages and draws, Lab is still likely to be really good. If the available villages or draws are weak, then Lab will remain the best option because of its consistency. If the villages or draws are good but expensive, then Lab might be the more economical option. In any case, Lab is still a valuable engine piece because of the consistency it provides. And yes, I know that Hunting Party is almost always better, but the chances of both cards appearing on the same board is miniscule.
Alchemist - This one possibly gets trashed even more than Lab. Yeah, it's expensive, but the Potion remains useful. The same arguments for Lab apply here: There might not be villages or terminal draws, or they might be weak. Whenever I don't go for this and my opponent does, I nearly always lose. The power and consistency of a top-decking Lab is very hard to beat. Maybe I just suck at building engines...
Den of Sin - I simply cannot understand why this is considered better than Lab. Yes, I'm aware of the amazing benefits: Gain to hand, can't be drawn dead, bigger hand at the very beginning. The fact remains, though, that if you're drawing your whole deck, which is something you should always try to do, you need two of these to do the same thing a single Lab does. In my experience playing with it, it's clearly inferior.
Caravan - I find it... a bit odd, or at least interesting, how similar this card is to Den of Sin but how it's nonetheless cheaper... and yet still considered overall worse. It's basically Den of Sin but one of the +1 cards gets moved to this turn instead of the next, and yeah, all those other aforementioned side benefits are removed as well. Now don't get me wrong, I don't think Caravan is super strong, and it's clearly worse than Den of Sin disregarding price. I guess I find it interesting that +2 cards this turn and +2 cards next turn are BOTH considered better than +1 card this turn and next turn. I guess draw is something you don't want to spread out?
Stables - I was definitely confused to see this higher than Lab in the new list. It's better than Lab if you can't trash your Coppers, but most of the time you can and should. The fact that this relies on treasures gives two ways it can dud: You can either draw a hand with all treasures or draw Stables with no treasures. Lab's consistency will beat it most of the time, I think.
Lost City - Lost City is great... but is it that much better than Vanillab? +2 actions is always good, but it's often going to matter less if you're already drawing a good chunk of your deck without terminal draw... which is what Lost City does. So is the village effect overall worth the on-gain penalty? I think it usually is, but I'm puzzled as to why this is so MUCH more highly regarded than Lab.