How do you create a free video game without a degree

The only thing a degree would do for you is show to others that you understand whatever it is you got the degree in. It's very possible for you to teach yourself about programming and game design. Some people don't have the self-motivation to teach themselves so they take classes about it, others take the classes to actually get the degree so that they can work for a company.

Open up Google and start doing searches about game design and programming.