In a strict sense, no.
In all practicality, yes.
Whether or not a degree is worth it is a never-ending debate among developers; my answer* is based on my experience and bias as someone with a computer science degree, and the next person to answer this question for you may say that I'm completely wrong. However, I think the answer is clearer for game development than other developer paths.
There are a lot of successful programmers in the world who do not have a computer science degree. Not counting coding classes in high school, they might be self-taught or have gone to a "code camp" or some mix of the two. But the most common career paths for programmers without a formal CS degree are web and mobile development. Many companies are willing or eager to fill Junior Developer roles with code-camp graduates because these positions do not require the deeper theory taught in a good computer science college—those code camps are focused on basic algorithms and data structures, how to use APIs and frameworks, and UX, and you can teach yourself web development even without them.
You may, a few years from now, decide that all that glitters is not gold and you don't want to be a game developer. If you finish your degree, you will still have more well-rounded experience and a better foundation for doing anything else software related than those without, so stick with it. Yes, having a degree and what that degree is in matter less the more experience and time you have in the field, but you need to actually get into the industry first. Do not forget to take an internship to get work experience and work samples to show.
* Source: Brian – Computer Science Masters Degree
You would need courses in software engineering and graphic design. It is good that you are thinking of a career in game designing, especially since the eSports industry is a $900 million* industry, and with the advent of 5G and AR/VR, it is about to expand.