many gaming companies require people to test and promote their games...you can try them only if you are good at games...you may even try to win some good contest that is played online like Wow, CS, DOta etc.... i am sure no one will pay you for playing those rickety flash games.....
To be honest , I myself don't want to such paid to paly games . I am already get addicted in computers games a lot and waste much time . I hate to get addicted in games, even someone pays me to do .
even, i don't any such sites, hope some one post a great site which pays there members for playing games
You can get paid for playing arcade games, and then write the description for it Some arcade webmasters pay for that.
If you are good in writing also, you can try reviewing the games. Do not limit yourself to play games only, you might get some part times with this but you cannot have this as a safe career...
there are 3 ways: 1/ very good at a particular game then participate in many tounaments for rewards - think of world of warcraft, final fantasy online, king of fighter or someth like that, starcraft 2. Many pro players make easily 100k+ a year just from reward money not to mention advertising etc 2/ Be a game tester for some companies in ca as someone mentioned. Apply for it and take ur chance 3/ Work for a game news company and u need to play them to write review, journal about them I h ve a lot of friends in MMORPG who have full time jobs playing games like this.
I hope this helps this is a thread for getting paid to play flash games. http://forums.digitalpoint.com/showthread.php?t=1396532