tranquility is correct that ideas on their own are not protectable. There is no good way to keep someone else from coming up with the same idea, or taking your idea, and developing it.
However, if you have an idea for a product and this idea builds off an already existing rights-protected product, you should not develop your idea and make a product. What you create could be looked at as a derivative of the original and would infringe on the original owner's rights.
If you think your idea is a great one and that the video game company could benefit greatly from it, you might want to sit down with an attorney in your area to discuss your plans. The attorney can help you get a non-disclosure agreement drafted that you can use in a meeting with the current owner of the rights in the video game.
Getting an appointment with the video game owner (or representative) could be your biggest hurdle.
If a meeting is arranged, you should have the NDA signed before presenting your idea. With an NDA, you can be somewhat assured that the rights holder will not take your idea and run with it without you.
Before even thinking of arranging a meeting, you should make sure your idea is, in fact, original. Your idea will need to be presented well - demonstrating to the video game rights holder the potential marketability and profitability of a product based on your idea, should your idea be developed. This will require a lot of supportive research.
In other words, having an idea is only the first step. There is a lot of work that goes in to getting an idea from the thought stage to the market.
Again, seek out an attorney in your area for advice on how to present your idea and get it to the proper people and how to keep it protected once it gets to them.
Good luck.