OP I think you misunderstand what a story is.
A story is a work of creative content that gives its author certain rights.
If you want to share a story, or a piece of written material you first declare your rights to it, and it up to the people you share it with to decide if they wish to break the law. In fairness this is the same risk that EVERYONE in the game industry takes: By sharing music, or models, or code or filmscript.
If you have a good storyline - put it down on paper.
If you have a good framework for a game - put it down on paper.
Stick a copyright on it that declares your authorship and ownership, and - like everyone else - hope that people aren’t douches and steal your stuff.
If you cant do that, or your story wasnt unique enough to be copyrightable, frankly you didnt have much to start with.
Please also be aware that you can’t copyright an “idea”. Everyone has those… You can only copyright the idea when it is in a tangible form: for example the idea for a movie is copyrightable as a moviescript.
I think you mistake “idea” with story, and are saying that you dont want to share your ideas in case someone steals them.
No. Nobody wants your ideas. Your ideas are not original HONESTLY. Plenty of people have had those thoughts before. The skill is the conversion of an abstract idea into a clever piece of writing, or script, or code or artistry or music.
That’s when people might want to steal from you. And thats when copyright applies.
I hope this helps.