You don't need a computer science degree to understand how to make games.
If you have prior programming experience, a semester worth of training can help in making the game easier. Or if you are super dedicated to programming, you can probably teach it yourself much faster. What is more important is that school won't teach you how to make a game. The programming courses can teach you the principles of programming that help you make a program. Game is just software. Even a simple implementation game can be more involved than your average console application.
What is more important is spending the right amount of time understanding the fundamentals of programming concepts and ideas and connecting how these pieces come together to make a game. Schools can guide you but if you are motivated and driven, you can learn it yourself. In the end, it is rewarding and challenging. The final results are worth it.
You can start with C++...But it is more advanced I would say in terms of learning game programming for that language. You can do loads of research of what issues you may be running into. But it is a learning experience, you will have some road bumps or obstacles in any language because it is just testing you how much you know about your language.
Java is a good language to learn. It has a built in Java graphics library so you do not need to find one. I would say everything you need to make the game happen is provided by the Java library. You just need to know how to use it.
I would not get caught up in the language. The language is just a tool. Find one that is comfortable. Eventually, you will need to adapt to a new comfort zone(that is learning a new language).
Don't just read books. Start questioning and discussing with people who are more knowledge about general programming or game programming. Just start doing small stuff-make simple games and be happy with it. As you get better at making games, start challenging a little bit more. Push yourself.
The knowledge from CS does help though I would say.
If things get challenging, start breaking it down to the point until it is understandable.
How to break into the industry: Interviewers like seeing a portfolio/demo/prototype/project. So if you have that, that MIGHT get you a job but it is not guaranteed. Just get something running. A project speaks louder than your degree or resume. Most people can't finish projects but if you can, you are ahead of the game which is why I recommend you work on game projects that are simple(which can actually be completed by one person)