Unless I'm mistaken, you're the one adding the own interpretation of what purpose an "exploit" serves.
If we follow your logic to it's conclusion there there can be NO cheats or exploits in any multiplayer game since all players can make use of the same game-mechanic.
The fact that things DO get classified as cheats and exploits, despite the fact that "everybody can use them", demonstrates the fallacy of the original assertion.
I'd suggest that a better definition of a game exploit would be "an unintended game mechanic which grants the player some advantage compared to their situation had they not used it"
For example, Bethesda games have a common "exploit" where you can tell an NPC to pick up an item, grab it at the same time they do and you both end up with the item.
So, you find one "Sword of Doom", tell your sidekick to pick it up, grab it at the same time, and you both end up with a "sword of doom".
There was one sword but now there's two.
You have gained an advantage that you wouldn't have if you hadn't made use of an exploit.
Already answered the single player game side, the game Devs can decide if you've gained an unfair advantage over the game mechanics. So yes you can use an exploit in a single player game.
Your suggested definition is very nice and well thought out, I like it.
However, we are currently working within the realms of the existing laid out definition currently, of which you need to have the advantage over the game (which Frontier is abstaining from saying) or another player. Currently, any player could do it as well - so that's even, no advantage to anyone.
As for the morality of doing it, that's another discussion.