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You can choose from wide range of courses offered by various institutes in India after completing your 12th.
Courses:
B.Sc in game art
PG diploma in Visual communications
Game art (core)
Game art (professional)
Game design, etc.
or
You can take some degree related to computer science or information technology, where you can learn the basics of coding and try to become a strong programmer. If you are good in coding either networking or writing drivers or developing games will become easy. Then focus on graphics and maths which is a lot used in gaming.
I had become game developer by mostly by practicing only. Develop one by one game and learn the concepts and all.
But nowadays big game engines are giving their source codes free, so acquire enough knowledge to understand it when you read their codes.

EE is the basic course, but with constant electronic use, in day to day engineering, the EE coursework is modified to EEE.
It's just like C & C+, where C is the basic programming language and C+ is an evolved and improved version of it.
Now, I never came across an institute or university or college offering these two courses simultaneously, i.e. both EE and EEE, because it's just isn't possible to draw a line between them.
Maybe some institutes offer EE and some EEE, but the coursework will be much or less same only.
Look at GATE, the only paper is EE not EEE, but now look at the syllabus, it completes the whole Electrical engineering and basic touchup on electronics engineering.
Same is the case in recruitment scenario, if PSU demands electrical engineer, they conduct exams for which eligibility is for electrical engineers, now this means a EEE lad can apply, but not ECE.

In the Department of Civil and Environmental Engineering at BIT Mesra, there are well established laboratories in the department. The faculty members are well qualified and are having degrees from reputed Institutes. They are actively involved in research and consultancy. The department had contributed a lot in the infrastructural and industrial growth in Jharkhand by providing technical expertise and consultancy. The following are the important research areas in which faculty members and research scholars are working:
Air Pollution, Applied Hydrology, Bioremediation, Composite Materials, Concrete Structures, Durability of Concrete, Geo-environmental Engineering, Groundwater Flow Modelling, Groundwater Quality Management, Heavy Metal Pollution, Intelligent Modelling in Geotechnical Engineering, Mine Slope Stability Analysis, Open Channel Hydraulics, Pavement Materials, Soil Stablisation, Solid Waste Management, Structural Dynamics, Wastewater Treatment, Water Quality Assessment.