You can still program games whenever you want. You don't need a college degree to do that. No one is stopping you from building a game right now.

However, you should get a college degree if you want to land a job as a game developer. +1 to the CS degree. Stay away from accelerated programming schools that have been popping out recently (e.g. General Assembly). They won't give you solid software engineering foundation.

Whatever degree you get, do not assume that school will give you all the knowledge you need to be successful. Colleges and universities are not (usually) trade schools. Studying computer science really means studying the "science of computation," not programming, though programming is definitely a part of computer science. Make sure you do lots of programming outside of your classwork, because you won't get nearly enough programming experience to compete even with other junior devs through school alone. As someone who went through a computer science degree myself, it's depressing how many people think just going to school prepares you for your career.

There are huge swathes of students coming out of CS degrees that got good grades, but didn't really learn to program and can't even identify (for instance) the difference between an array and a linked list. Don't be one of them.

It would be great for me to have a job that is related with game dev however the market for games in our country is just meh. So I assume that game dev related job will give a pretty low salary which is not what I want since I want to give back to my parents. So I did a pretty small research and found out that software engineer currently is the best option for me, Still I don't want to spend my life following the human life cycle (Study > Work > Family > My Kids will study > They'll work > and the loop goes on) I want to have fun by doing what I want to which is to make fun games.

2 Options really, if a low wage is what you are trying to avoid:

1) Relocate. Given you develop above average skillsets, have a very good english (or whatever the language is where you relocate to, for Japan japanese would be preferrable for example), really look and fight for jobs and have some luck, you might find a job in a region of the world where there are more job openings, and where game devs are better paid on average (be aware though that there are most probably still shitty jobs with low wages there).

2) Get a well paying dayjob. Make game development your hobby. Live with the consequences of having less free time than your friends besides developing games. You don't need to be inside the AAA Industry to make games. You do not need to have an AAA games career to become a successfull Indie (though I heard it helps, a lot).

You don't need to be successfull to have fun developing games!

As others have said, don't expect too much from College / university. You are doing it for the degree. While it might teach you some good basics, most of the important stuff you will learn on the job. Or, even better, in your free time prior to applying for a job. And depending on what you are applying for, you can build a good portfolio from these hobby projects (many game dev positions are easier to get if you can show an awesome portfolio, that can include programming jobs... nothing tells "I can program AI" better than a prototype with your self written AI code in action).

Do the college for the degree, but never forget to build your skillset above and beyond what college teaches you.