This is the best reply in the thread.
I've also graduated with CS many years ago and spent a career programming and working my way to VP level in some big companies. Hired many a fresh graduate like you.
There are millions of CS grads being churned out of middle rate schools. Very few really want to program. For those that excel, a degree is not a necessity, and usually it just teaches good techniques. But the good ones have a passion for it without being pressured. They will keep up with the latest tech, think about code in their free time, and just generally perform many times better than everyone else.
The request for an existing portfolio isn't just to show that you have experience. It's because people who are good programmers will be doing it whether or not they are being paid! A good hiring manager can spot the bullshitters.
As Ryk said, think carefully about your career here. You can also take your programming skills and apply them to other fields you might care about more, so it's not a lost cause. But re:gaming, I will also say that I worked with veteran game programmers, and the general perception is that game careers is some of the hardest and least rewarding; every employer knows there are 10 people willing to step into your role, so they pay less and demand more.
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I should also add, if you are considering grad school, you might think about studying something else that you are passionate about but which has software application. Many industries would value a person who knows their industry and also software.