For me, game mechanics matter when they get in the way of fun. For example, some of the baroque and obtuse dice-pool mechanics fashionable in the late 1990s meant it was next to impossible to have any meaningful idea of your character's chance of success at any given task, which could be very frustrating in play. The worst ones had probabity curves that were so screwy they made the numbers on the character sheet almost meaningless. Another example is combat systems that bog down in play, especially when there's a large group. If it takes four hours to resolve a barroom brawl, your system is broken.