I have been trying to figure out how to use the media keys on my keyboard to control Google Play Music for a while. It turns out that Chrome is set up to listen for the media keys, but the X11/Gnome were capturing these events and not propagating them to the browser.

TLDR: Disable the Play/Pause, Next, and Previous keyboard shortcuts in the Gnome Keyboard controls.

Screenshot of Gnome Shell Keyboard shortcuts