I'm a patent attorney for a video game company, which means I have to play video games in order to understand what is new and potentially protectable. It's a fun job, took me a while to get here – I got a degree in chemistry, then worked as a research chemist, then a pharmaceutical consultant, then went to law school, then worked at a law firm, then worked at a tech company, before being fortunate enough to land my current job. But you're probably thinking about a different type of career path.
My brother was a researcher at a life sciences company with a salary and benefits and job security, but he quit to take a minimum wage jobs answering phones at a large video game company, and eventually worked his way up to testing video games, worked in tech, then recently was head of engineering at a small gaming company.
Either way, there is probably no one true path, but the real question is what you want to do with your gaming skills. Do you want to design games? Code games? Play games professionally? Or just look for bugs? If it's the latter (which is usually what folks mean when they want to test games), then consider that it's not all fun and games: http://www.businessinsider.com/what-its-like-to-be-a-video-game-tester-2015-6
On the other hand, if you play a lot, and play with friends, then you may be building up a fair store of knowledge on what makes a game good, retains players, and ultimately makes money. In which case, the video game industry has a lot of opportunities available. It's not an easy industry by any means, but it sure is fun!
If you're really good, and somewhat entertaining, you may consider streaming on Twitch. Or providing reviews on YouTube. If you're good enough at MMOs (e.g., DOTA, LoL, HoS, HS) to compete, then consider going into eSports, which some universities are actually recruiting for. If you just love video games and the industry, and want to be a part of it, while still playing games, then consider coupling your passion with another discipline, like computer science, game design, business, law, finance, or others.
And don't let anyone tell you that playing video games is a complete waste of time. It worked out for this guy: http://www.theverge.com/2015/5/22/8643065/mark-zuckerberg-video-games-good-for-kids
But also remember that balance is important in life.