There are now a lot of career options in case you are interested in sports and games, but dont see yourself becoming a professional sportsperson.
Sports Medicine is a growing field.
Performance Analytics is another area if you are interested in technology
Professional Player Management
Sports Management major aligns best with your interests, however it is a very competitive industry. If you want to pursue your passion for sports and games, and also keep other options open, then a major in business management or marketing may give you the best of both worlds. You'd be more marketable with other opportunities and also position yourself for any sports related jobs.