One the the biggest problems with your layout now is that the rocket is the most visually attractive objects on your page. I would suggest reducing the size of the rocket and header. This will also give you more vertical space, so users with smaller screens won't have to scroll down as much to see the games. As you can see with my paintover I added some text under RocketGen, this should be used to explain the site really quickly. This will give new users a very quick way to get to know more about your site especially since it is a gaming one. The logo feels very cheesy web 2.0 overdone logo. Try a few different versions of the logo, and perhaps have the 'R' in rocket and 'G' in gen to be capitilized. Also try working the rocket into the logo type.
I agree with you about the round edges, it feels like it would work better with your the rocket image. For the individual game boxes, the text is way to close to the edges of the box and picture. Try spacing it out a bit more. Also instead of having a "play>>" link, make the title of the game and the picture the link to the game page. This is more intutive and gives the user a larger area to click.
The tab navigation is a good idea. I would add those rounded corners in for each of the tabs. There is a large white space in between the tabs and the gray body background. I would remove this completely. For the left navigation the rocket trail was too close to the first option. Also the links were too close together, add some vertical space inbetween each.
All in all its a good start. A few small changes here and there can really make a difference.