Specifically, I'd like to know how or why one game would have it in any more or less abundance than any other.
It's an interesting spin on the old question, and completely legitimate. Sure, some would say that role-playing is just taking on the part of a character and playing out that character's actions in a hypothetical situation, and thus the rules themselves don't matter. You could, theoretically, role-play Monopoly or Settlers of Catan. And to some extent, I have to agree with that, because I tend to RP in my head when playing boardgames.
That said, there's a reason we fork over wads of cash for sets of rules. I mean, if the rules didn't matter at all, we could all just save ourselves lots of money and utterly destroy the business side of the hobby by adjudicating uncertainty through flipping coins or popular vote or DM fiat. But for most of us, that wouldn't scratch our itch, would it? In this, I think the Forgites are right. Rules matter. Setting matters. And the two should, at the very least, not work at cross-purposes to one another.
Allow me to dig deeper into that definition of role-playing. For me, role-playing is taking on a character, inhabiting that other person while exploring an imaginary landscape that is simultaneously internal, social, and physical. Add in the “game” of RPG, and I'm not just exploring that landscape, but tackling the challenges that landscape presents.
So, with that definition in mind, I can begin to come up with a list traits that a game ought to have to “do it” for me. First, the rules must promote and support verisimilitude. I want to submerge myself into the character and the worlds that character explores, and the more I can do that without being asked to fiddle with gaming bits, the happier I am.
This has a lot of consequences for my choice in game. For instance, some games of the Forge school attempt to remove the DM by sharing the world-building duties among the players, or even making it part of the game. This, though, is horrible for me. With the world so uncertain and often times so random, I never feel I can trust it enough to explore it, but must stand back, watching out for where it's going to suddenly transform itself again. I'm much happier with a GM who has a strong sense of what the world is about and how it works. With a good GM, I'll trust a bit of zaniness, because I know, while I might not be able to say how, the whole thing holds together like a tapestry, and if I follow the threads long enough, I'll find how they all weave together.
It also means that I don't want any more rules than I absolutely need. If I'm looking up a rule in a book, I'm not enjoying my character. If I'm using the rules to overcome a challenge instead of using my character or the setting, I'm too deep into the game and too far from my character to get what I want from an RPG.
So why don't I get rid of the rules altogether? Because I need the rules to reinforce the verisimilitude. The rules keep things consistent, dependable, and understandable. This is especially important for the fantastic elements of the game. Magic, fictional technology, and the supernatural need a structure they can hang on, so I can trust that they'll work in a consistent and believable way.
I also need the rules to deal with things that I can't just play through easily at the table. Combat rules are useful because I don't want to try jumping around the dining room swinging swords at my friends. Rules which abstract certain economic realities mean I can focus on the fun parts of being an interstellar smuggler and don't need to worry about keeping track of supply and demand for certain commodities across a hundred dozen markets. Arguing with a spreadsheet is only fun for me if the character I'm playing is an accountant who, you know, spends his days arguing with spreadsheets.
And this is why my game of choice right now is Labyrinth Lord. Combat is abstract, and with a few tweaks it doesn't disturb my sense of verisimilitude. Character creation is also very abstract, so I don't end up with a character who can barely do half the things I'd mastered by the age of 16. Does it have some annoying gameisms? Sure does, but I can live with most (such as escalating hit points) and can change those I don't like (such as the limitations of class, and race-as-class) very easily. More than all of that, though, is probably that I know this game backwards and forwards. I rarely need to look something up. I can gin up a ruling at the drop of hat, without fretting overly much about how this might impact other aspects of the game, and spend more time in the world and less time in the rules.
This is why 3e was such a let-down for me. They'd purged the game of nearly every annoying gameism that had hobbled D&D over the years. But they did so at a cost of such a rigorous and complex rules structure that I just couldn't get away from it. Nearly every sort of interaction now had a rule governing it. I was sad to leave it behind, but I just couldn't enjoy a 3e game the way I did older versions of D&D.
Even though 4e's design philosophy seems to be at least 90 degrees off from 3e, it's got a lot of the same problem for me. There's far too much game standing between me and my character. Keep in mind, this is a completely subjective thing. For someone else, 4e might be the perfect fit. If I was forced to really master the rules of 4e, it's possible I could achieve the level of comfort I'd need to pass through those rules and tweak them so that I could inhabit my character like I'd prefer. But I'm not sure how I'd keep food on the table and a roof over my head while I did that. Labyrinth Lord is working great for me so far, and a game with 4e's complexity would really need to be something exceptional to justify the time and effort I'd need to bash it into a shape I'd enjoy as much as I do Labyrinth Lord today.