Part of your issue is that the python executable that blender uses and the one you develop on outside are two different executables, and they do not share any package/libraries: install something with one, the other won’t see it.
You should also understand by now that you don’t want to play “copy the folders by hand”, because when installing a package, maybe other dependencies are also required.
pip knows, let
Oh and lastly, distributing such a game is not really straight forward, unless you distribute an executable version, in which case you will have to run
pip inside your release before uploading it for others to use.