In order to use picture-in-picture, you must first move your mouse cursor over the video screen in order to get the options bar to show up.
Once you have the options bar overlay, you have to press the red-circled icon to activate picture-in-picture.
If you use Zaurus in Firefox, you will not see that button. Instead, you need to use the native picture-in-picture mode.
You can activate this to press the button on the right side of the screen.