In the interest of setting the stage for the discussion, let's quote a real book about games: Akio Matsumoto and Ferenc Szidarovsky's Game Theory and Its Applications, found here:
"In formulating a mathematical model of a decision problem, there are two conflicting tendencies. In one hand we would like to include as many variables, constraints and possible consequences as possible in order to get close to reality. However, on the other hand, we would like to solve the models, so they must not be too complicated. In creating a decision making model, we have to identify the person or persons who are in charge, that is, who is or are responsible to decide. There are two major possibilities: one or more decision makers are present. In order to decide in any choice, the set of all possible decision alternatives have to be made clear to the decision makers."
It is in this that we see the core elements that make table-top role-playing more than a superficial reading of giving descriptions and giving answers.
First, the variables, constraints and possible consequences that can be taken into account and the consequences resulting therefrom can transcend the number of variables that can normally be managed in a model . . . because human beings can process incredible amounts of information and make agreements on the spur of the moment to account for variables that a pre-fashioned program could not predict or for which the programming feat necessary would be impractical.
Role-playing is not managed through a lack of rules, but through precedent - the understanding that as decisions are made in game, those decisions are expected to apply for all future circumstances that follow a like occurrence. Like the way that the law is tailored for a complex society that is constantly changing year by year, role-playing is vastly more flexible than a rule-system can account for. But understand, precedents are rules. Judges and judgments in the law are subject to precedent and every DM in every game that has ever made a ruling puts into force something that will be called into question later by the players if the DM fails to obey that same ruling. Some old school role-players understood this; others did not. Those that did not ran games that did not last long. Games that lasted did so on the basis of an ever-growing legacy of rulings that made clear to the decision makers what the boundaries were, as the quote above stipulates.
Secondly, role-playing provides for the presence of not one, not two, but multiple decision-makers, more than or potentially equal to any other game or program that has ever existed. All players and the DM too are "responsible to decide." In turn, this places a far higher requirement upon the responsibility of presenting choice than might exist in a game like monopoly.
This is also the reason why tabletop continues to compete for time against video games. While most of the people in my life are hardcore gamers, they're willing to give that up as soon as I'm willing to run. Why? Because unlike video games or board games, role-playing is mutable. The potential for changing the goals of the game, adjusting the rules as necessary, tailoring the context to the participants and so on can be potentially done in minutes of "programming" - something impossible in any video game, no matter how detailed or expensive the game is. The game is pre-made. Role-playing is present-made.
Those who argue that the format for decision-making is clear and defined between players and DM, that my role is this and your role is that, fail in the extreme where the potential of the game exists. Anyone at the table is a resource for decision-making that deserves acknowledgement. The players, as much as the DM, should feel free to propose rules for situations that they feel are unclear where it comes to their abilities to make a decision. The players, as well as the DM, exist to ensure that precedents are followed and supported, because in a legitimate game both players and DM have worked together for symbiosis of play. The players, as well as the DM, are part of the game's constructive process.
Without this symbiosis in place, we have a shit game. It does not matter what tradition has been, or what old-style players played - this is the future of the game, because this is the only sustainable future the game can have.
Those who fail to learn this lesson will forever lack for players. Those who do learn this lesson will have a self-sustaining game for the rest of their lives.