OP is looking at games through a modern lens rather than thinking about what games were back then. We think of games today primarily as a story with interactive elements, with a few exceptions for abstract games like those in the puzzle genre which are not really a part of the culture zeitgeist that is 'video games'. However, before Donkey Kong, video games were not stories at all, and for a long time, any story was secondary to the game itself. It really wasn't until the 90s that the stories for games became a critical part of their identity.
The idea of a sequel is something we think of for books and movies. And back in the 70s and 80s, sequels actually being good were rare. Outside of a few series, sequels did not carry much hype and didn't make as much money as their predecessors. Movie sequels often had smaller budgets and completely different actors and directors. They were like a completely different movie. Calling something X 2 would not instill any kind of confidence into a consumer in that period at all. The expectation for what a sequel was was also a bit different. Nowadays, we typically think of a sequel as being a continuation of the first story. But traditionally sequels were just another story set in the same world with some kind of connexion to the first story. The Lord of the Rings is a sequel to the Hobbit, but it doesn't continue the story from the first. It is a completely different story.
The story structure of modern sequels actually comes from serials, which were books (and later short films), that told an over-arching story in multiple parts. We would call them 'sagas' now, to make them seem more epic and important, but fundamentally they really are just serials, regardless of how ambitious in scope they may be. Star Wars and The Godfather both had successful sequels whose stories were structured like a serial: they maintained a strict continuity with the first film and focused on the characters of that first film. They didn't go off into too different of a direction. Most sequels now follow this story structure (the media most likely to not be now is, ironically, video games; e.g. Final Fantasy games are largely self-contained or only loosely related to other entries).
So, changes in the film industry are certainly a part of what would effect how sequels would be perceived in video games, but it would take quite a long time for that to trickle down. In the mean time, the biggest video game industry in the 70s and 80s were arcades. Owning an arcade required significant investment, as the hardware was quite expensive. Some people rented machines while others bought the systems outright. Regardless, the actual owners of the machines quickly found that it was seldom worth buying a machine when a new hot game would come out months or weeks later, and also players would quickly get too good at the game.
Conversion kits were the solution to this problem. These kits allowed operators to keep the sturdy parts of the machine like the monitor, cabinet, and speakers, while swapping out other parts: the board, the signage, etc. Some kits were completely new games. For example, early Donkey Kong cabinets were famously just Radarscope conversions. But the second type of kit was used to address the problem of popular games becoming too easy, which I'll call the sequel kit.
An example of a sequel kit would be Ms. Pac-Man. Ms. Pac-Man is fundamentally the same game as Pac-Man but is more difficult and has some extra features. It famously changes the title and art in a unique way: the protagonist is now a girl. Midway could have just called it 'Pac-Man II' and be done with it. Many developers did do this, e.g. there was a Space Invaders II. But giving a more unique name was a way to attract people, instead of just a boring number. It soon became an assumption that a sequel to a game was just the same game only harder or with more features, at least in the arcade. This eventually spilt over into computer games and consoles, where the idea that any sequel was the same game plus minor variations.
But a problem in the console market was that the business model didn't carry over. On consoles, players only needed to buy a game once. In an arcade, they needed to pay in quarters, and an operator would just withdraw or convert an old game into a new one and continue to collect money. This was not the case with consoles, and players who bought a first version of the game would usually not buy its 'sequel' version. There are a few notable arcade-style sequels on platforms like the Famicom, but these were usually very popular games sold as a budget title, special promotion, or some other special consideration. Super Mario Bros. 2 (Japan) is probably the most well-known example. The Japanese market was more receptive to this, so most of these games were exclusive to that market.
Looking at the American side of things, we can start to see how changes in the market would lead to a different kind of sequel. The NES was incredibly popular and effectively saved the video game industry from collapse. And part of this was Super Mario Bros. And with Super Mario Bros. came a lot of marketing, tie-ins, toys and merchandise, and other things about the world of Mario and not just the game itself. It was the first game series that really captured people's interest in its world and story rather than just its gameplay. Nintendo, therefore, knew that it could cash in on more games featuring Mario, but it also knew that it could not just be a rehash of the first game. This actually went off into two different directions at Nintendo, the Japanese side and the American side. The Japanese Nintendo would eventually develop Super Mario Bros. 3. While we may, today, think of it as being really similar to SMB1 and SMB2 (J), for the time period, it's quite different compared to how an arcade sequel would be. The American side would get a reskin of an entirely different game called Yume Kojo as its Super Mario Bros. 2. The idea of the black sheep sequel was born.
Now Nintendo, as well as other companies, really started to focus more on story for its games. So during the mid to late 80s we see a number of famous series get their starts. Early sequels like Zelda II and Castlevania II ended up with very different gameplay compared to their predecessors, but by the 90s the fear of having a sequel too similar to its predecessor had started to fade, and we see sequels that are much more similar like the Mega Man games. By this point, people started to think of video game series as basically the same as that in other media. The cultural expectation for Zelda III was on the same level as that of RoboCop III. Unfortunately, only one turned out to be good.
