Update - the more advanced extension (Spotify Web Extension has remote-control abilities. It uses Google Cloud Messaging to setup a push channel. When you want to remote control another computer, my server wakes up your extension using the channel, and then sets up a relay between the two (a WebSocket connection on both ends).
Make sure to set a keyboard shortcut for easiest use (go to the chrome extensions page (type chrome://extensions in the URL Bar) and on the bottom click “Keyboard shortcuts”. Enjoy!
I’m working on a more featurefull extension that will allow you to do more than just skip tracks :-)