Find different sites, forums, etc. where people might share an interest in gaming. Contribute to the discussions and include a link to your site where it is allowed. Also, get the word out through Social Media. Create your own Facebook, Twitter, etc. pages. Good luck.
Gaming is not really my niche. I focus on free money making opportunities. But if you do a Google Search for gaming forums, you'll find a whole bunch to look at.
What kind of games? Like flash games or video games? Just an FYI flash games our going away because of game apps for phones.
Try advertising it on Facebook. Target the audiance right and people will come and like your website. Just build your own audiance.
You can try Facebook and Affiliates or CPA people who can promote your game. If it's a mobile game, there are many apps which will promote it for you for a small fee. Definitely try that.