Simply put, game mechanics refer to rules for determining the outcome of random events, and of actions with a considerable chance of failing. For example, you don't need rules and dice rolling to have your character walk or run, but you'd need them if your character wanted to outrun a chaser or walk with a severe leg injury. Game mechanics deal with the likely-hood of him succeeding against unlikely odds.
That said, the main role of game mechanics is not to determine the success or failure of actions, but to serve as a guidance of which actions a character would be inclined to perform given his skill set. Would your character fight his way out of the palace or would he sneak out? Would she seduce the high priest or intimidate him? By determining which course of action is trivial and which is hard, skills mold the character's behavior even without a single die being rolled.
Remember that the subjective aspects of the game – story, scene, mood, interpretation – are the most important, and game mechanics are just a tool to help processing the game world. Shinjudo mechanics were designed to be simple and intuitive as to free players to focus on what's important.