I am writing a story for publication that has one of it's key features is these other worlds/universes being the basis of the videos games we see in real life. As such I was hoping to have 2 books in the series features worlds from Nintendo Games Legend of Zelda and Fire Emblem, but not claim any ownership to these inclusions. I did look up Nintendo's copyright claim, but I can't quite figure out if I can legally do this. Is there a way or do I need to abandon the idea of using the game's worlds directly?
Nintendo has a history of using legal actions to shut down fan projects.
When they come after you, it will be a civil lawsuit, not a criminal one. That means you need to pay the expenses for your defense up-front. If you can't afford proper legal defense, you will very likely lose the lawsuit, even if you might actually be legally allowed to do it. Even if you are able and willing to pay for proper legal counsel, Nintendo will likely have far deeper pockets and be able to afford much better lawyers than you do. So this is a battle you are very unlikely to win.
If you are lucky, they will just insist that you cease publication. When Nintendo's lawyers are in a particularly bad mood, they might get you to pay litigation.
IANAL, but this is one of those questions where you can start out by asking, are other people doing this. If not, there is a good chance that the answer is that you can't do it either.
This is essentially what is called a tie-in. Your book would be tied into the world of the games. People who play those games would be a natural market for your story. (In fact, I suspect people who play the games would be pretty much the only market.) So, your books would be profiting from Nintendo's IP and if there is a way to stop people from profiting off their IP, Nintendo would do it.
From which we can reasonably (though not definitively) conclude that it someone else is doing this, then there probably nothing Nintendo can do to stop them, and if they are not doing it, that is almost certainly because there is something Nintendo can do to stop them.
But don't overlook the obvious here. Instead of trying to avoid trouble with Nintendo, take the whole project the Nintendo and propose it to them. Media companies love tie-ins. It is a way to extend their brand and therefore to make more money from it. And if Nintendo likes the idea, then they will take care of the publishing process for you. If the books sell, they will probably contract you to do the same for other titles. And since game/movie tie ins are a thing (its is beyond me why, but go figure) your book might even become the basis for a movie.
TL;DR: Since you almost certainly can't beat them, join them.