Join big gaming forums where game lovers get together and discuss about different games. Promote your game site through your signature. If your site's games are good, your will definitely get a lot of stable traffic from there.
Create a Facebook page for your website. Build a good number of fans there and drive them to your site.
Also if you have some budget for the marketing of your site, you should try PPC ads especially in Facebook. Most of the game lover likes to be in Facebook.