Can I fork another persons repo twice into my own account?

In your case, I would suggest going with submodules. However to answer your exact question, here's how you should proceed.

1. Start by creating Jeremy/MyShooter and Jeremy/MyRPG on Github. Keep them empty.

2. Clone your origin project on your system, twice, giving it different names

   $ git clone http://github.com/Bob/CoolFramework MyShooter
   $ git clone http://github.com/Bob/CoolFramework MyRPG
   

3. You now have 2 different local repos pointing to the same origin. You should remove the origin and point to yours as a remote:

   $ cd MyShooter
   $ git remote remove origin
   $ git remote add origin http://github.com/Jeremy/MyShooter.git
   $ git push -u origin master
   

4. Don't forget to do the same for MyRPG

From the sound of things, you are using a framework within a game you are creating. If you are just using the framework and not changing it, create a new project for your game and include the framework project within it as a sub-module.

Assuming you are not modifying the framework, you should not be forking it. Forking a project is for modifying (often with the intent of submitting your fork to be merged back into the source project).