Why can't I choose output sound for each application?

I am using dual monitors, and I want to be able to play a movie with sound on the TV (through vlc or something) and then play youtube or some games with my headphones on my laptop. Is there anyway I can choose what hardware each application uses?

I've tried using pavucontrol, but am not given an option to change the output device.

EDIT:

jeggy@localhost:~$ sudo aplay -l
**** List of PLAYBACK Hardware Devices ****
card 0: PCH [HDA Intel PCH], device 0: ALC665 Analog [ALC665 Analog]
  Subdevices: 1/1
  Subdevice #0: subdevice #0
card 0: PCH [HDA Intel PCH], device 1: ALC665 Digital [ALC665 Digital]
  Subdevices: 1/1
  Subdevice #0: subdevice #0
card 0: PCH [HDA Intel PCH], device 3: HDMI 0 [HDMI 0]
  Subdevices: 1/1
  Subdevice #0: subdevice #0

You could try PulseAudio Volume Control (pavucontrol ).
sudo apt-get install pavucontrol

Then select output device like so.

I think we are overlooking the simplest answer here, I think you only have one sound card, and correct me if I'm wrong... but don't you need to have more then one sound card to be able to use different output devices.

In your question you wants to play the sound from one program thru the headphone output witch is probable connected to your "only" sound card, and one programs sound thru the speakers connected to the computer, witch once again is probably the "only" sound card you have. And has far as I know you can't play one sound to the headphone output and another sound to another output on the same card.

I don't know witch version of ubuntu you are using but in the picture you have provided there is a tab called "Output Devices" you can check there if you have more then one sound card. I have provided a screen-shot of how my looks, observe that it lists 3 devices but i only have 2 there is two "Bulit-in Audio" and i can not play different sounds to them.

It might be clearer to run "aplay -l" in a terminal

Example:

aplay -l

yealds ...

**** List of PLAYBACK Hardware Devices ****
card 0: Intel [HDA Intel], device 0: ALC271X Analog [ALC271X Analog]
  Subdevices: 1/1
  Subdevice #0: subdevice #0
card 0: Intel [HDA Intel], device 1: ALC271X Digital [ALC271X Digital]
  Subdevices: 1/1
  Subdevice #0: subdevice #0
card 1: Generic [HD-Audio Generic], device 3: HDMI 0 [HDMI 0]
  Subdevices: 1/1
  Subdevice #0: subdevice #0

there it is easier to see that there is two cards card 0 and card 1

So if you only have one soundcard my advice to you would be to buy a USB sound card and connect your headphones to that. and then use duffyducks or andys answer to choose output device