While I think discussion of genre can be helpful, the fuzziness of the definitions of genres (and especially sub-genres) and the lack of applicability in certain situations with regard to TTRPGs can lead to more heat and less light. So, going back to Greyhawk, it is fundamentally a Sword & Sorcery setting, but that doesn't mean that you are required to play it that way. The influences are there, but whether you engage with them or not is your choice.
While this is fair, there's something to be said for the faults of swimming upstream (or, ahem, relieving oneself upwind, as it were). If what you're trying to do is deeply, fundamentally at odds with the written setting conceits, you're probably going to have a bad time. Athas is an intentionally dark, gritty, low-fantasy survival-focused setting. Trying to run a classic "clean" high-fantasy (e.g. "Paladins & Princesses") game in Athas is...well, It's not that you
can't make it work, but why would you ever
want to? Likewise, the Sixth World setting of
Shadowrun is a fantasy cyberpunk corporate dystopia; you can choose to play it low-level or high-level or anywhere in between, but you're almost certainly going to have a bad time if you try to play a "hearth fantasy" type game--and, likewise, you're going to have a bad time if you try to play a black trenchcoat ruthless chromed-up street sam in Humblewood.
Yes, genres and styles suffer from the sorites paradox, the "I know it when I see it" problem. But that doesn't mean the "influences" can always be brushed aside and ignored. There are greater and lesser degrees of influence, greater and lesser departures. A really
strong influence, like the cyberpunk of SR, is going to resist departures that might be otherwise relatively mild. A dramatic departure, like trying to run a magical-girl anime story in Athas, may always be a square peg no matter how much you polish the round hole.
Avoiding those sorts of fool's-errand efforts is precisely where genres and styles and other loosey-goosey things are useful. They're signposts to help point you toward the things that, even if they aren't a
perfect fit, will at least not fight you every step of the way.