This latest circular one wouldn't scale well at all, and doesn't really say "video game music" to me... except maybe in a Gyruss sort of way.
But I like that you're working the musical element into the logo itself versus fading it into the background. Have you considered playing up the video game component by introducing some old school arcade styling? (see attached) You could also use some very generic arcade-looking characters. (a spaceship, an alien, etc)