On a Mac you can use the Automator.
Create a new document of type "Service" in the Automator. Choose Service Receives Selected Text: no input. Add a "Run AppleScript" action.
Adapt the following script to your purposes:
on run {input, parameters}
tell application "Google Chrome"
set foundTab to missing value
repeat with currentWindow in every window
if foundTab is missing value then
repeat with currentTab in every tab in currentWindow
if currentTab's URL contains "play.google.com/music/listen" then
set foundTab to currentTab
exit repeat
end if
end repeat
end if
end repeat
if foundTab is missing value then
set foundTab to (make new window)'s active tab
set foundTab's URL to "https://play.google.com/music/listen#/ap/auto-playlist-thumbs-up"
delay 1
end if
execute foundTab javascript "document.getElementById('player-bar-play-pause').click();"
end tell
end run
Save your script with an appropriate name such as "Toggle Google Play Music on Chrome", then go to Services Preferences, find and add a keyboard shortcut. Automator -> Services -> Services Preferences.
This finds any open Google Play Music tab and attempts to click the play button, to either pause or play. If no tab is found, it launches one in a new window (you could modify it to instead create a new tab in any existing window). Obviously, you have to pick out what URL you want it to go to.
Note: whatever URL you do go to in a new tab/window, it won't start playing automatically. If you figure out how to do that (I ran out of time), please post a comment letting me know, or just modify the script to include that.