Assumptions

How important are they?
Every rule system I am familiar with contains built-in assumptions including how the "world" works. The world's original role-playing game, the one I actually prefer over all other editions and variations on the role-playing game theme, makes several assumptions based on its sources of inspiration and the preferences of its authors. The underlying assumptions in a game is not something I have always looked at or even been cognizant of, but now that I think about it, should probably be something we gamers pay attention to. The underlying assumptions can greatly influence how we see a system, labeling those games "good" when the games assumptions fit with our preferences and likewise "bad" those games that are based on assumptions we disagree with.
The White Box is good example. Authored by miniatures gamers and aimed at the wargaming hobby, The Little Brown Books assume new players are already familiar with the basics of tabletop wargaming: taking turns, moving figures across a table, rolling dice, inflicting casualties, calculating morale, etc. What the authors include in the Little Brown Books are suggestions for using wargames in a fantasy setting or world - one that assumes magic works, monsters are real, and heroes can advance to super-heroic skill proportions.
Other built-in assumptions in White Box D&D include the cast of player characters - humans are the predominant species reflected by their lack of level limits. Elves, dwarves and hoblings are playable characters, but are limited in how powerful they can become and therefore presumably less attractive to play long-term - a fact which may make them less common in the milieu than human player characters.
White Box assumes all creatures are aligned with either Law, Chaos or Neutrality and therefore have built-in allies, and enemies. This is a useful concept for wargames when choosing up sides is part of the basic preparation for play. It is assumed the game will make use of various maps to control movement and to keep track of location. Time and its passage is considered important in the game session and the campaign or series of connected sessions. Magic comes in two flavors, arcane and divine as reflected in the two spell casting classes, magic users and clerics. The rules for magic, including memorization of spells are very similar for each class and there are overlaps in the spell listings for the two caster classes.
All role-playing games make assumptions. The ones I am familiar with draw certain details from the real world, from history and from fictional sources. Even the mechanics which aim to simulate certain physical realities consistent with the real world make assumptions about how physics, chemistry, psychology, and other dynamics work. Assumptions, and certain abstractions based on those assumptions, are present in all simulations, games and otherwise, for without them there are simply too many variables to be accounted for.
In a fantasy game there is the question of magic? How does it work in the game? How common is it in the setting? How is magic viewed in society? Most games have either an implied setting (White Box is one of these) or a specific default setting (for example classic RuneQuest is set in Glorantha) which is connected to the assumptions the game makes. Even so-called "generic" systems such as GURPS is based on a number of assumptions. GURPS claims to use how things work in the real world as the basis for much of its mechanics, but at the root of how we view reality are many assumptions which game designers then make more assumptions about when they decide how much data to include in their real world model. Ultimately, how well our personal preferences match up with a game's assumptions seems to help determine how much we will like and enjoy that game.