Salt To Taste

Medieval Flavoring
With the subtitle, Rules for Fantastic Medieval Wargames Campaigns... Mr. Gygax nominally claims the white box as a medieval style setting because it seemed to him that much of the sword & sorcery literature which inspired the game has a somewhat medieval flavor or feel to it. I also think the origins of the game in a variant on the medieval campaign run by the authors influenced the use of the title word "medieval". To be sure, reading the works of R.E. Howard, J.R.R. Tolkien and others I find they are full of kings and swords and warriors on horseback. The default white box technology level (leaving aside magic) seems more medieval compared to an historic timeline. Perhaps this is as Mr. Gygax had in mind.
The white box rules certainly do not deal with social caste, fealty, the medieval church or any of the social and cultural aspects of medieval society. It seems rather more a blend of heroic myth and the modern western cultural ideals of working hard, getting rich and building one's own little "kingdom" in a world of fantastic creatures and magic.
The referee can add additional mechanics to model medieval society and make the chosen milieu feel more chivalric and courtly as a part of their individual customization of the game. Many published settings and a few subsequent rules have taken this approach over the decades since the white box made its appearance. Early games such as Chivalry and Sorcery and King Arthur Pendragon have tried to take the medieval world setting more seriously by adding extensive rules for social background and chivalric behavior thus encouraging play that more closely reflects a medieval mindset. Harn is a setting that draws heavily from medieval history for it's gritty, realistic feel and Harnmaster, the rules written specifically for gaming in Harn carry the theme forward. In such rules, glory, honor or reputation, romance, family and other achievements often take the place of acquiring wealth and hit-points as a measure of successful play.
My Personal experience with such games is that it is difficult to find players who are willing to put forth the effort needed to alter their thinking to a consistent medieval mindset. In other words, I have found that a little salt goes a long way when flavoring a medieval setting. (I like the analogy of salt because the middle ages was a barter economy and salt was valuable and often substituted for coin.)
Referring to kings, dukes and milady, calling oneself a knight, and building a castle all seem to be quite appealing, but that's often about as medieval as many folks want to go.