The big link in pre-3e Exalted between the mechanics and the themes is that Exalted is an exception-based game system and the characters are exceptional.
Exalted spends a great deal of time explaining how the nitty-gritty details of the game world interact with the rules. It has detailed rules for combat that include stuff like how to determine when crippling injuries occur, tracking bleeding out, sepsis, dedicated charts of healing times which drive home how big a deal being hurt is. It has complex combat rules to determine how bad it is to be outnumbered (very bad) and all sorts of situational details about position and cover and all kinds of other details.
Then it cheerfully says, over and over, that none of this applies to you. Because you are just that awesome.
You know, in the old fashioned “fear not” version of the term.
Exalted characters are designed to stand above the rest of the world, to not be concerned with its petty problems. The game teaches you about how lethal disease and poison and starvation and exposure are and then gives you either automatic immunity to those effects or extremely cheap access to those immunities.
Even the exceptional performance of the Exalts is made even more exceptional by the specific Charms of the main character type: Solars. The rules include specific steps on how to determine what happens when two magical exception powers come into conflict and then peppers all the Solar Exalt’s Charms with clauses that make them win regardless of these rules. For example; when two Charms come into conflict you have a roll off with relatively mild dicepools. Any Solar Charm where such a roll-off would occur gets such a hefty bonus that the roll-off is a formality, the Solar is going to win it regardless unless faced with overwhelming competition. This follows with defensive abilities as well, with the rules specifically noting that in a defense vs offense contest the defense always wins; but leaving exceptions where defenses are Inapplicable and thus can’t be evoked. Then the Solar Charms systematically remove all those exceptions.
The impression from the mechanics is not just that you stand above normal people, but you stand above even the extraordinary. You are pinnacle.