Many d&d monsters are based on myths. It's more likely that humans have encountered or seen into the Upside Down before. Or had the odd encounter (the Demogorgon was capable of traveling back and forth, either naturally or because the gate in the lab made reality thin). Humans talk about them in myth for thousands of years and they're eventually turned into a game. The thing is, the kids don't really know anything about these monsters. They don't know what the Mind Flayer wants. It's like when they compare El's power to the Force. It's not the Force, it's just an easy reference that they can go on.
The kids run out of steam in season 2 when everyone asks how to kill the Mind Flayer and they don't have answers. The creature in the Upside Down is not a Medium aberration who eats brains with a tentacle attack. If the kids were into something different, like Lovecraft, it'd be just as easy to call the Mind Flayer Yog-Sothoth.
The Mind Flayer in the show targeted Will because he was caught between the two worlds. He spent more time than anyone in the Upside Down. And it's affected him uniquely. It's possible that his powers will grow (for instance, he might begin to be able to travel back and forth at will, rather than just seeing into it). But it's also possible that because the gate is now closed, his link to it will be closed as well.
You are right that the Mind Flayer will probably target Eleven now (assuming it doesnt move on from Hawkins) If it cannot reopen the gate on its own, Eleven (or one of the other psychic children) will be a priority. Which will make finding Brenner a big deal.
So I don't really believe the theory that the kids shape the Upside Down. I just think they're able to cope with it because the rules of heroes and monsters are still meaningful to them compared to the adults who live in a world of bills and small town malaise