Greetings!
Bachelor of Science in Game Development is designed for students interested in game development programming at the highest level, including computer science and computer graphics professionals retooling for the game industry.
As far as eligibility for game development and design courses are concerned, it varies as per the type of course that you opt for as well as the institute that you pick for it. For instance, a certificate level course in game designing can be taken up right after completion of Class 10 from any stream. Whereas, for diploma or graduate level courses, you have to clear Class 12 Board exam from any stream. For masters, the eligibility is graduate degree, preferably in a technical field.
Some of the top colleges providing this course are:-

• BhartiVidyapeeth University, Pune
• Maya Academy of Advanced Cinematic (MAAC), Mumbai
• Arena Animations, New Delhi
• Zee Institute of Creative Arts, Bangalore
• iPixio Animation College, Bangalore
• Animaster Academy  College for excellence in Animation, Bangalore
• Academy of Animation and Gaming, Noida

Career as a game designer and developer is a very exciting one. You can opt to work in a variety of genres ranging from action, sports, fantasy etc. Also, the gaming industry has seen a great growth in the Indian markets over the last few years and has provided several job opportunities for gaming enthusiasts. The field also offers some lucrative salary prospects for people with good talent and experience. Not to mention that pursuing a course in this field helps you convert your hobby into your job.
Hope this helps you understand the course better and gives you detailed information.
Good Luck!