I was thinking about this more, and something came to mind.
Another reason why I believe "system" does matter is because (as I said earlier) I am someone who believes mechanics and fluff have a relationship with each other.
As an example, I play GURPS a lot. One of the benefits to GURPS is that it is modular. In particular, there is more than one way to handle magic. I fully believe that the magical style I choose for a game does greatly change the feel, tone, and style of the game I am running, and likewise creates a different relationship between crunch/mechanics and fluff. Admittedly, I typically use the default magic system found in GURPS Basic Set because I find it does an adequate job of covering a lot of what I want to do. However, for some game types and genres, Ritual Path Magic is a far better fit, and using RPM instead of the default magic system greatly changes the tone of the game, the mechanical aspects of magic from a player point of view, and the way that the in-game world works from a character's point of view. If I were playing a Supers game and my character idea was a hero powered by magic, I wouldn't use either of the magic systems I mentioned, and I would instead build my character's 'spells' using innate attacks, advantages, and disadvantages; this too would have a big impact on tone, feel, mood, how both the player and character interact with the game and game world, and various other things. Even though my choices of game system is exactly the same in all of these examples, my choice of mechanics and "system" within that same toolkit (GURPS) greatly changes the enjoyment of the game and (in my opinion) the suitability of the mechanics in relation to the story I'm trying to tell.
I fully believe that I could attempt to tell the same exact story three times, choose a different magic system for each time, and the story -even though it's the same story- would be portrayed very differently because of that change. A lot of the major plot points would remain the same, but a lot of things would change to. As said already, the way players would interact with the game would be different. Also, the way characters interact with the world around them would be different, and this would in turn change the thought process behind making choices both from the perspective of the character an the perspective of a player controlling said character. Note that in all three tellings of the story, I would also be using GURPS, but changing an aspect of the system which would in turn change the game and produce different results.
In this context, I'll again bring up the original Dragonlance novels because they were (in the beginning) written around how D&D worked at that time. I fully believe that if Dragonlance were written today and written around how D&D 4th Edition works that the story would not turn out the same way; it wouldn't be logical for the characters to even approach the world they live in the same way because of major differences in how the physics engine (if I can borrow a video game term) of the world they live in would change. From a reader's perspective, the story would change as well because of the fact that the world the characters are in would function differently, and the characters themselves would also function differently. The major parts of the story and the general plot might very well be exactly the same, but the details in between would be different, and it's the small details in between which often matter the most.
