Try to implement the game Asteroids without a thought about data structures, just start programming it procedurally as it comes to you. See how far you get in, say four hours. Find a graphics library, of course.
Then, use a very simple object oriented model, where everything on-screen (asteroids, ships, enemy ships, shots) has a draw method, a move method, a create method, and an I'm-hit method, together with logical internal state like position and velocity. See how far you get in the same four hours.
Note how much easier it is to do the second way. That's the power of data structures (and, admittedly, some simple oo ideas, deployed in a lightweight way).
This is the power of designing before you code. Nothing to do with data structures. Data structures are part of the design but you're focusing on the object oriented design aspect.
You know, I put in a caveat anticipating this objection, but since you raised it, let me offer the following counterpoint:
You could implement the approach I described in a language without any OO support, and still come out ahead.
Just do it in plain C using function pointers for methods, and write your own dispatcher. Or, do it in assembly (I implemented this approach in PDP-11 assembly).
If you do it this way, it really is all about the data structure -- the methods are subordinate to the data structure, acting just like other state. You could even change the methods after objects have been created -- for example, swap in the "evasive maneuver" move method once you fire on an alien ship, so that the alien goes from lazy drifting to taking evasive action.
Then, use a very simple object oriented model, where everything on-screen (asteroids, ships, enemy ships, shots) has a draw method, a move method, a create method, and an I'm-hit method, together with logical internal state like position and velocity. See how far you get in the same four hours.
Note how much easier it is to do the second way. That's the power of data structures (and, admittedly, some simple oo ideas, deployed in a lightweight way).