Just drag the tab out to its own window. Then you can minimize it and Chrome doesn't consider it to be in the background.
Random aside: I just noticed that after you drag the Gangnam tab out to its own window, then you can open other tabs in that same window, and it doesn't put the Gangnam tab in the background anymore. But if you put the tab/window back in the original set of Chrome tabs, then it will.
Random aside: I just noticed that after you drag the Gangnam tab out to its own window, then you can open other tabs in that same window, and it doesn't put the Gangnam tab in the background anymore. But if you put the tab/window back in the original set of Chrome tabs, then it will.