First, you can try to be a beta tester for the big video game companies. This is probably not the easiest thing to do. To earn the top dollars these companies usually require years of testing experience and some programming knowledge. That doesn't mean you can't get a job from them. You just won't be playing the coolest, top games.
Second, you can find one of these companies that are putting games on Facebook or just making a new site for a game. They aren't the most glamorous games but you still can get paid to test them out and give your feed back.
Third, start writing game reviews. You can start your own website and write your own reviews about the latest games you have played. If you have found cheats or hidden treasures you can post those too. Create a walk through. To get a domain name is cheap and easy. You can find cheap hosting too so you keep your costs down. Invite others to offer their thoughts and any cool things they have found while they were playing. To make money this way you would need to get into posting ads on your site for different companies related to gaming. You can try Google AdSense for one. Amazon.com is another. If you want to try GameFly.com you need to have quite a lot of visitors already established and have a pretty good functioning site to pass their application process.
Another way you can earn money playing video games is through some different sites that allow you to play games to earn credits. You do certain tasks on the site and earn credits. If you refer someone you earn credits. You keep building up your credits and doing the tasks they ask you and you can convert those credits into cash. These sites are usually a game within a game. Some are like medieval games. You play a couple of child like games to earn your credits. You take those credits to build your army and kingdom. You battle others and take them over to earn more credits. All of these credits you eventually take and convert into cash for yourself.
All of these are ways you can use your gaming addiction to earn yourself some money. I am not saying you will become rich doing this. These are just ideas for you to try.
Best of Luck!