Downloading pygame games without pygame?

Yes users need a Python interpreter and a reference to Pygame to execute your program – since your game is written in Python and uses the third party library Pygame.

That said, you could consider to use

• cx_Freeze,
• pyInstaller or for example
• py2app (for Mac users)

to freeze your Python scripts into an executable and to make a standalone application which your friends could download and execute without having Python and / or Pygame installed on their computers.

The Pygame wiki gives you an example how to compile a Pygame app to a standalone windows application using py2exe.