I define a game as a formal ruleset. By formal I mean that the rules are complete in-and-of-themselves and there is every effort made to well define every possible state of the game world at any given time during the game.
By those standards, you might judge a roleplaying game not much of a game. And it’s this sense of formal completeness that bars it from matching our definition well. A roleplaying game is played in such a way that the written rules cannot possibly cover every possible play-state.
But by another analysis, you might say that it’s the sincere effort of every would-be Gary Gygax to define the formal rules for every play-state that actually happens when a group of college buddies huddle around a table to slay imaginary bad guys. It doesn’t matter that the Book with the Big Red Demon doesn’t have written rules for how to do a somersault between a guy’s legs and hamstring them. It’s dressing around the d20 roll. And if you look at it in this way, a roleplaying game is a notoriously long-winded tribute to formal completeness. Some games manage to achieve completeness quite succinctly (Costikyan’s Toon is an excellent example), just as chess expresses huge depth with 6 different pieces.