For a rousing introduction to the concept of intertextuality, I recommend this talk by Sørina Higgins, “Little Loosed Dragons: Intertextuality in Beowulf and the Inklings.”

And applying this fruitful area of research to video games is well underway, as this post from “The Musings of a Digital Humanist” suggests.
Those will give you a sense of the academic uses of this term. Basically, intertextuality deals with the ways in which texts relate to one another. In video games that borrow the name Excalibur for a magic sword, or call something or other the Yggdrasil, or make a reference to the death of God, for instance, we might see references to legends, myths, and philosophical ideas, but we might also hear echoes of other games which have done something similar. To track the specific texts at play, then, would be to point to not only any number of Arthurian, Norse, or Nietzschean retellings, but to a whole range of video game forebears, too.

So that even if I haven’t got around to FFXIII, and couldn’t tell you why Lightning Returns, I still might be better able to appreciate what the game is going for here if I have ever looked up that strange word Yggdrasil. Or if, when I did, I realized that I’d seen a picture like this before, as a kid, in the National Geographic Picture Atlas of Our Universe. So that like some cosmic tree, intertextuality’s roots and branches extend as far as we can conceive. The paths our thoughts run along, of image and association, direct quote or oblique variation, will inevitably find out some, but not all, of the possible connections.
Besides the usual epic RPG suspects, though, what other games come to mind as being particularly fruitful loci of intertextuality?
Super Smash Bros. and Kingdom Hearts, for me, were the obvious places to look, and so that’s where I’d start a course on this topic. Visual novels like the 999/Virtue’s Last Reward series seem rich as texts and full of connections between them. When I asked Ben for his take, he suggested two games by Daniel Mullins, Pony Island and The Hex. He also mentioned The Beginner’s Guide, which I remember watching as a playthrough on youtube awhile ago.
With those as suggestions, we might let students decide for themselves where to go next.
NB: To practice intertextuality with the pros, Foundations in Critical Reading and Research at Signum U is probably the “best value course” at this incredibly affordable institution. Taking any course there opens up access to their digital library, including Project Muse and JSTOR. Zotero is a great way to keep track of that research; here’s a training, again courtesy of Sørina.