A couple issues. HDMI won't support 144hz. It might get you to 75hz at 720p, but that won't work for 3D Vision anyways. If that projector is truly 144hz, you'll have a Dual Link DVI-D or Displayport connection on it. That will have to be used, though with the use of 3DTV Play may support 3D at 60hz and 720p over HDMI.
The next issue is that you have to make the projector your primary display to game on it. You can do this by going to Windows "screen resolution" screen and adjust which monitor is the primary one. It might be possible to use HDMI through Nvidia 3DTV play, but I'm not experience with that and it would limit you to 30hz or some sort of compression mode if the projector supports it.