NOTE: After noticing that the 3 components of Nippon's Trident formed a Venn diagram, I realized that Nippon's Trident could actually be applied to sequels and continuing story arcs in general. So the name Nippon's Trident doesn't quite fit anymore. Later I'll come up with a better one. For now, keep in mind that while I only exemplify Anime here, you should try applying it to stories of all mediums.
Videogames are unique in that they are part of both the technology and entertainment industries. Because of this, games generally share aspects from mediums in both industries. So every once in a while, it's worth examining how the techniques of other mediums crop up in games. So let's look at anime and manga for a moment. Many Japanese games use a manga art style (like anime) and many others will borrow anime's tropes, making Japanese videogames relation to anime and manga immediately apparent. Note I am not what one would call a "fan" of those mediums. I don't actively seek anime to watch or manga to read, nor do I keep up with current series. However, I have absolutely zero qualms against the mediums themselves and will watch shows at others' recommendation (usually after doing some kind of research on what I'm getting myself into). Some of these series, however, make my skin crawl. Namely the ones which seem to be competing for the coveted Longest Story Ever Written Award.
HOW TO WIN THE LONGEST STORY EVER WRITTEN AWARD
For whatever reason, sometimes a writer feels the need to extend their work's story beyond their initial story plan. Unfortunately for the writer, she or he may have already written their story so that it ends in a very conclusive manner. So in order to drag out the length of the story, writers will have to resort to using what I call Nippon's Trident. Nippon's Trident is more or less the antithesis of Occam's Razor in that a writer will avoid a simple conclusion in order to elongate a story. Writers typically do this using a combination of three methods (hence the name tri-dent as opposed to Yari) all based on where the plot extension is derived from.
1 - Continuing from the previously established endpoint
Surprise, surprise, the first method is also the most logical one. This is when the final events of the previous story directly lead to the events of the following story. Assuming the reader/viewer finished the previous story, they should immediately understand most of the premise of the new story.
2 - Building on existing story detail(s)
The second is also fairly obvious. Here, the writer chooses to explore a detail that was previously mentioned, but ancillary to the central plot. Once again, this method of extension is very audience friendly and shouldn't require much additional exposition.
3 - Introducing something without prior indication of its existence
And finally we have the cheapest means of extension. This is little more than just making something up. It's not inherently bad and most certainly is not lazy in that it requires far more creativity than the previous two methods. However, because the audience lacks any sort of ground to stand on besides perhaps shared characters, it's generally saved for film sequels or new volumes in a book series.
Now, as I previously stated writers always use a combination of these three methods. This is not due to some stubborn refusal, but because it's logistically impossible to single out these methods, due to their interconnected hierarchical relationship.as illustrated by the Venn diagram below.
The named combinations of each of the three previously mentioned methods thus read as nearly direct combinations of the three methods. The lower number explains "what" the new plot detail does while the higher number explains "how."
Continuity - continues from previously established endpoint by building on existing story detailsSpontaneity - continues from previously established endpoint without prior indication of its existenceIncompletion - builds on existing story detail(s) without prior indication of its existence*? - We'll get to that a little bit later
Together, these combinations of the 3 previously stated methods make up Nippon's Trident. Each achieves the effect of extending a stories plot, but they all do so a little bit differently and all have slightly different unintended consequences, depending on the effectiveness of their incorporation into a canon. In no particular order, let's start with the one that doesn't rhyme with the other two.
INCOMPLETION: "I WILL NOW SHOW YOU MY TRUE POWER!"
Surprisingly rare, incompletion occurs when the writers add details to some existing part of the plot or story that now makes it relevant to or the focus of the main plot. This generally occurs in shonen anime when the protagonist gains some super power as a result of some never mentioned before power/ blood/trait they purportedly "had all along." For example in Dragon Ball Z, during the Frieza saga, it is revealed that Saiyans grow more powerful when they survive near death experiences; what doesn't kill them literally makes them stronger. This results in Goku mustering the power to become a Super Saiyan and defeating Frieza. This was never even alluded to prior to that point, and yet it becomes a key part of the rest of the DBZ series.
A more egregious example of Incompletion occurs in Naruto and its follow up series Naruto Shippuuden. In one of the first five episodes, Naruto learns that Sasuke's village was burned to the ground by Sasuke's elder brother Itachi. Around fifty episodes later, we learn that Itachi burned down his village to join the hereby never before mentioned organization Akatsuki. AND THEN, more than one hundred seventy episodes later, we learn that Akatsuki is actually planning to take over the world by performing some unheard of ritual that makes them the new main antagonists.
In the worst case scenario (like the Naruto example above), an Incompletion is basically an ass-pull in disguise. The writers make something up mid-story, but try to make it look like it was planned from the beginning. However, an Incompletion is ultimately just a twist by a different name, so if a writer can use it without seeming contrived or like a deus ex machina, then it shouldn't be obtrusive and can re-contextualize the entirety of a story.
CONTINUITY: "BUT WAIT, THERE'S MORE!
This is as straight of a sequel as you can get. More details are added to the story in order to extend the plot. In Shonen anime, Continuity generally entails: Introducing a new threat/conflict somehow related to the previous main threat/conflict, but inexplicably more powerful/dangerous. It usually just extends the existing plot and leads to power creep.
Tengen Toppa Gurren Lagann does this repeatedly throughout the show. The first villains you learn about, the Gunmen, come from the Spiral Fortress (the next villain), which is subservient to the Spiral King (the next villain) who repressed the world's spiral power because of the threat of the Anti-Spiral (the final antagonist). Gurren Lagann however, justifies using this means of extension by establishing near the beginning of the show that spiral power is limitless. As such, the protagonist could, by the show's logic, continue to grow stronger along with the new villains.
Due to the simplicity of its implementation and its connection to existing story threads, Continuity is rarely criticized. However, by its very nature Continuity cheapens the experiences that came before it, by minimizing their significance with new pressing story details.
SPONTANEITY: UH, UH, EVERYONE'S NOW A PIRATE! *PLEASE DON'T FIRE ME
And last, but most certainly not least, we have Spontaneity. As with the other techniques let's look at the trend in Shonen anime (no, I will not stop picking on this genre #dealwithit). In this medium, writers will usually concoct a completely new threat that's more powerful/dangerous than anything the protagonists have dealt with before. The threat must never have been spoken of prior in order to be truly spontaneous. And, just like Continuity, it almost always leads to power creep.
Using Dragon Ball Z again, after the Frieza Saga, a character Trunks, literally appears out of nowhere using a time machine (apparently those exist as well) and says that Androids are being built by a maniac and will destroy the world unless Goku is cured of a disease he doesn't have yet. And this kickstarts the Android Saga. It has absolutely zero relation to the saga that came before it and has no allusion to any of the events prior except for the fact that Trunks is a pre-existing character's future son. However, it occurs chronologically after the events of the previous saga, and can therefore theoretically be loosely justified as canon.
Spontaneity can seem like the ultimate in ass-pulls in that there is rarely ever a logical justification for it to be used other than to extend the plot. Although, sometimes more plot is all an audience wants.
SO WHY THE "SKIN CRAWLING?"
Looking at the popularity of the shows that use(d) Nippon's Trident ad infinitum, Naruto, Bleach, One Piece, DBZ, etc. one would be hard pressed to question what the problem is with relying on these techniques. From a business standpoint, they are clearly useful and lead to great success. But, on the philosophical level, these techniques can be problematic.
When learning how to write a story, one of the first things taught is that a writer be careful not to include too many significant events in their story. The first reason is that more details leads to a more complex narrative, which may confuse your audience and cause disinterest. The second is that the meaning or moral of whatever story you are trying to tell becomes increasingly diluted, the more story details you insert. Now one might argue that, entertainment doesn't have to be meaningful, it just has to be entertaining. This is true. However, time and time again certain anime and manga prove that a series can be both meaningful AND entertaining, so it doesn't make much sense to only focus on one and not the other. Additionally, excessive length still leads to the complexity/disinterest problem, which runs directly counter to the goal of being entertaining. So, like all techniques and tropes, Nippon's Trident is not inherently good or bad. It merely "is."
"OKAY, WELL WHAT ABOUT THE '?'"
That "?" is the rare occasion when a series incorporates all three elements of Nippon's Trident into a single continuation. Its definition would be: Continuing from a previously established endpoint, by building on existing story details, without prior indication of its existence. Basically, the plot continues from the end of the previous story by reexamining an existing part of the canon with some thing or knowledge that was never alluded to before. As of this point in time I can't list a single anime that uses this method of plot extension, but if you can find one by all means suggest it.
"ALRIGHT, ALRIGHT I GET IT! NOW HOW DOES ALL THIS TIE IN TO VIDEOGAMES?"
The Kingdom Hearts series is probably the most successful abuser of Nippon's Trident in recent history, so exploring its connection to its various sequels provides the strongest example of this technique gone horribly awry.