The Music Beta Skip simply exposes a Browser action button that will skip the current track if one is available or will open a new tab with the Music Beta Web App in it if none is already available.
This Music Beta Skip controller can be used side by side with the Music Beta Play/Pause Browser Action available here: https://chrome.google.com/webstore/detail/lblkffdkmmemjagfanapkgkogilikbad.
The code for these extensions is open source and available here:
You can see what was added to individual releases here:
You can file bugs and feature requests here:
You can use this other group to discuss usage of these extensions: http://groups.google.com/group/music-beta-controller-discuss
And you can register to this one for communicating with other users of these extensions: http://groups.google.com/group/music-beta-controller-users