Well, any game without social mechanics is probably a good example. Some games seem to lean on the idea that players and the GM will resolve social conflicts... socially. The system seems to expect them to roleplay the entire thing with no mechanical support or for it not to come up at all. This may be an intentional element of the design or it might be an oversight.
Some systems hide their responsive tools. Using World of Darkness as an example, the game provides a simple combat engine which generates a static number (called "Defense") which is subtracted from most incoming combat rolls. However, Defense is not designed to model an active effort to avoid incoming danger. Specifically mentioned dangers, such as magical powers or traps, include their own Attribute + Skill roll to avoid being caught but little is said for general avoidance. It's easy to default to the Skills provided, making Dexterity + Athletics the go to "avoid large thing landing on me" roll but the game doesn't actually tell you to use that, you have to make that assumption.
Now, World of Darkness actually intends for this kind of thing in it's design. It defines a large number of skills and tells you to combine them with Attributes to form die pools for various taskes. The book provides dozens of potential tasks (ones common to the default game style), but not nearly all of them. This is a middle ground between the options presented in the episode: it's house ruling but within the designed space of the game.
Were you leave this is when you discover a task to which no Skill is clearly suited. For example, horse riding. Would that be Wits + Drive? Dexterity + Athletics? Presence + Animal Ken? I'm not sure. It probably depends on circumstances and the game provides you with no advise on that specific task because it's likely not one the developers though to include for a modern gothic horror experience.
(Note: In some World of Darkness settings a "Ride" skill is, in fact, added to the game, solving the above problem; I think my general point still stands).