Role-playing games are perceived as complex due to their volume of rules. What really makes RPGs complicated, though, is the relative dynamism of these rules and the degree to which they sit in the text. In other words, the rules of a game you must know in order to play an RPG are not limited to those which are printed in the rulebook.
While this of course varies from game to game, it can be generally stated that a board game will contain all the rules necessary to play inside the box. This is not always true with an RPG. Given the significant breadth of concepts that a game could potentially cover, RPGs have usually needed a GM to establish a more concrete set of boundaries which make up a campaign. The key here is that what the GM is doing, from writing the world to tweaking the mechanics to actually running the game, involves making and enforcing rules which are supplemental to those actually written in a book.