Then using our ears to experience the music in the movie is also not diegetic. The mechanic is just like our ears. It's how we experience what is happening in the fiction.
No. The mechanic
is not our experience. Period. It is not in any way
the thing in your head being imagined.
It is a pointer. An indicator. A menu screen, if you like.
A menu screen can be diegetic or not. Consider, for instance, when JC Denton is reading an email from a computer he hacked into. That's diegetic, because the thing the character is doing (looking at a screen in order to read a piece of text)
is in fact exactly the thing the player is doing (looking at a screen in order to read a piece of text). Even though this pops up as a menu screen, which we typically assume to be non-diegetic,
Denton himself would see it as a menu screen.
Conversely, when I hit the escape button to bring up the overall game menu, that is clearly non-diegetic. Denton is not
seeing a menu with a screen that says "Save Game", "Load Game", etc.
The dice
are not in, nor of, your experience of the world. Dice are a mechanic which determines the answer "yes" or "no" depending on whether the resulting value, with various modifiers, is greater-than-or-equal-to some number, or less than that number, respectively. At no part of this
mechanic did the character roll dice, look at numbers, compare totals, or verify; to them,
it is simply an action, and the result is inherent and automatic. They know what the one and only result could be as it is happening. The dice do not do that. The dice don't say
anything at all about WHY the answer is "yes" or "no". Just
that it is "yes" or "no". (I say "yes" or "no" because different perspectives change what the result is in terms of success vs failure. E.g. if a wizard forces a bulette to make a saving throw, and the bulette "succeeds", then the Wizard "failed" to apply the effect; but if we cast it as "yes" or "no", then the question is more easily understood symmetrically: did the bulette avoid my attack? Did I avoid the Wizard's attack? yes/no.)
The dice are not your ears. They are not your eyes.
The GM is your eyes, your ears, your every-source-of-information. The dice, at most, simply answer yes/no questions.