It's a logo. Not a banner/ad/self-explanatory image. It's not intended to represent games, much like, for example, the apple logo doesn't represent computers and tech stuff. Had I wanted to make a banner which implied gaming, I always could cut and pasted some screenshots together.
That said, you are right, perhaps I should have made something more game oriented. But I still believe this will suffice.
Here some resized versions. I am concerned that the smaller ones become unreadable.

150x150

100x100

50x50