Class 11

Hello Anirudh,
You won't get any specialisation option right in class 11th. I would recommend you to choose science and keep computers as a subject in your class 12th. After completing your class 12th board examinations, you can opt for B.Sc, B.Tech, or BCA for your graduation.
A game requires different kinds of programming. Front user interface, backend database, encryption, and other programming tools depending on the game. You will be taught about these languages in the graduation stream. Once you've completed graduation, you're all set to develop your own game.
I hope it helps. If so, kindly upvote this answer.
If you've any further questions, kindly revert.

Hello Kiran,
After completing class 12th, you need to appear for various entrance examinations. I would suggest you to appear for IIT JEE and AIEEE. These two entrance examinations provide admissions to IITs/ NITs and other government colleges, which are cost-effective.
I would also suggest you to appear for individual state examinations (OJEE in Odisha, EAMCET in Andhra Pradesh/ Telangana, COMEDK in Karnataka, etc.). These exams also guarantee you good colleges and serve as a backup in case things don't end up the way you've planned for IIT/ AIEEE.
Every state has its own share of good engineering colleges. So, don't underestimate or overlook them. They can prove to be vital. The more the entrance examinations you appear for, the more the options you will have for choosing colleges.
Certain private colleges like SRM, KIIT - Odisha, GITAM - Vishakhapatnam and ITER - Odisha conduct their own entrance examinations. You can opt for these as well.
After the results of those entrance examinations are announced, if you have a valid score and rank, you can attend the counselling procedure for the respective entrance examination. During the counselling procedure, you can select a college of your choice and the branch of engineering.
I hope it helps. If so, kindly, upvote this answer. If you've any further questions, kindly revert.