Try some of the following: (at least one should work)
a) Dragging the video window to the second display before selecting full screen.
b) Go into the 'displays' system preference, and drag the menu bar from your computer screen, to the tv screen (in the pref pane), which will make the TV you primary display, and thus the video play full screen there.
c) Select 'mirror displays' from your monitors menu to show the same content on your computer screen and your TV.