First, I don't know anything about the Indian game job market, so everything I'm going to talk about relates to the US game job market.
Second, there is a HUGE difference between working for a large AAA company and a small indie studio. Indies do whatever suits them and the hiring process is often based on friendships more than credentials. So I'm going to focus on the topic of getting your first game dev job at a large company.
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It is important to realize that any industry changes over time and either a job's status (pay, clout) diminishes or the barrier to entry requirements will escalate. This is because careers perceived to be "good jobs" are the ones people flock to. More applicants means hiring managers can be more picky and demand increasing levels of qualifications. With that in mind, I'll go over what I've seen from various generations of first time devs and where I see requirements going now. (Here I'm using the term "generation" very loosely as some of these changes occurred over a few years rather than decades.)
The first gen of game devs often didn't need either professional experience or academic credentials to get hired - just an ability to do the job. I've met plenty of veterans from this era who had no formal training and were completely self-taught.
The next gen was required to show at least some form of either professional experience or academic credentials, but it didn't necessarily have to be game-specific. I've known devs with degrees in fields as diverse as child psychology, Russian lit, and sports medicine. As long as they could code and had a degree, they were good. This is also when professional coders from non-game fields had an easy time shifting into game dev without any game dev experience.
The next gen was generally expected to have a degree in a related field (physics would be considered "related" because it is STEM and they often write code to run experiments, but you would mostly likely be funneled into a job as the "physics engine programmer"). At this point, professional coders had to start showing that they had worked on something game-related, even if just on their own time.
The next gen was where things started to get heated. You were expected to have a degree in a related STEM field AND show some experience working on a game. This was the era of pushing everyone into making "mods" and building portfolios - even if you were a professional coder from a non-game industry.
The next gen was where hiring requirements got TOUGH. As an entry-level dev, you were often expected to get a degree in either comp sci or a game dev specific degree, AND you had to go to the "right" school. Some companies would throw away any entry-level resumes of graduates from colleges they had "blacklisted". (Colleges I frequently saw blacklisted included Full Sail, the various "Art Institutes", DeVry, ITT Tech, and some state colleges. BUT that doesn't mean you couldn't get a job at other studios with these degrees and typically no one cares about your degree once you have professional experience.) Meanwhile, some companies would ONLY hire entry-level devs from specific colleges or had arrangements with certain colleges to funnel the "best" students from those institutions into their entry level positions. (Colleges I've seen attain this status include MIT, Digipen, Stanford, University of Washington [UW], and UC Irvine.) Additionally, you were expected to have a "portfolio" of game projects to show (which was usually your class work). A workaround at the time was to make your own game and release it as an app so you could claim to have "professional" experience - even if it didn't make any money. Professionals from outside the game industry had a very hard time crossing over and, when they did mange to break in, they were often expected to take a serious reduction in both seniority and pay. (I've heard hiring managers claim they preferred to hire new grads over outside professionals with more than 3 yrs experience because it supposedly required "extra work" to un-train "bad habits" they may have picked up from working outside of games. This made it especially hard for veterans to break in, even with stellar credentials.)
Right now, there is this on-going debate as to whether or not it has become necessary to have a degree specifically in "game dev" or "game design" rather than just a general degree in comp sci or a STEM field. Increasingly, colleges and universities are offering game-specific degrees and the game industry increasingly needs entry-level devs to have more specific knowledge than general degrees offer. (Many University comp sci programs rely heavily on scripting languages and don't teach C++ or core concepts like writing memory managers.) Even for companies that don't intentionally give preferential treatment to certain colleges, I've seen many of them joke that they are beginning to fill their ranks with graduates from places like Digipen simply because those "game degree" graduates are more likely to have the skills the studio is looking for.
Either way, having a portfolio of games you made is necessary to get a dev job in the industry. But it is no longer sufficient to simply release a game into the world and call it "professional experience". Now you generally can't get away with that unless you can show decent download/play stats, you got some media buzz, or you actually started a company and can show you turned at least a small profit.
Parting Notes:
1) Realize that "breaking in" doesn't guarantee you a good career. This is a volitile industry and many devs leave in the first 1-5 years. Most devs will find themselves out of work at some points in their early career, sometimes for 1-2 years. You have to prepare yourself for that.
2) These are just generalities. Everyone is unique and has their own path in this industry. I've known devs who were out of work for years and now are senior devs at top-tier studios working on award-winning projects. Being dedicated, deliberate in your actions, and smart about your career can get you almost anywhere (issues of social bias and discrimination are still a major factor that can limit someone's ability to rise up in this industry).