I have been writing down the plot of my game and I notice that it seems like something that could easily have the Pokemon aspect of the game taken away and the plot would still make sense. Does this mean that the plot of the game doesn't need to be a Pokemon game and if it doesn't then how would I make it more necessary for it to be a Pokemon game? For context what I currently have for the plot is that you play as the sister of a young trainer who is mugged by mobsters who is now looking for revenge against the people who hurt her brother. This would lead her to discover that the organization the mobsters come from is run by a government politician. Somewhere along the way I also want to have a certain mythical Pokemon be used by this organization and politician. Is there anyway I can make Pokemon more dependent to this plot than just that?
Not really a problem, in fact it's flexible, and all official games have a mixture of mon-focus and other narratives. In most cases, mons are used as a means to an end. Be it Team Rocket's plans, or any other Team for that matter, or even the concept of sports competition itself (winning the League). If you took away mons, and it was something like basketball, it would still apply. Why? Because that's how RPGs are structured. So instead of Battles you'd have dunking sessions and the Dunking Championships. If the story was all about creating the ultimate mon, it's still something akin to creating an ultimate
insert thing here and use it for something.
Here's some examples that might help you incorporate mons.
The Gamecube Pokemon games were about thieves, an evil mayor (and in the sequel, the man behind the scenes who was funding him and a certain evil organization) yet everything revolved around "Shadow" mons and how to get them back to normal.
Gen 5 was the most JRPG-ish of all, yet the focal point of all the subnarratives were mons (and mon ownership and control) as well as mutual bonds and harmony.
Sun Moon was about the concept of invasive species in the form of wonky UBs.
One way you could do it in your case would be to touch upon
what it'd mean if the government in place was a government run by mons and the legendary was behind it all? That would put mons in the epicenter of the discussion, and would make for a nice plot twist at the end. It would also be extra fun if the team that was helping the government was anti-pokemon.