Your current HDMI 1.3 projector cannot be used for 3D if it is not a 3D projector. The SBS signal will show up as two images side by side, that is correct, but it is not the glasses that convert it into 3D. When you put that signal into a 3D projector, you then turn the 3D mode on and it will split the two views, and interlace them and stretch them to full screen. It will then show a full screen image for your left eye, followed by a full screen image for your right eye, then repeat continuously. The 3D glasses sync with the projector so that when the projector is showing the image for your left eye, the glasses block your right eye from seeing the image, and vice versa. I should also mention that the 3D video you are seeing is not full resolution. A full 3D source will have two 1080p images side by side or one on top of the other, fed over HDMI 1.4 to the 3D display. The video clip you are looking at is two 3D images that are half their normal resolution so that they can fit together on a single 1080p frame. When your 3D display receives this signal it upconverts the picture. In doing this, you can play the SBS 1080p video clips with a regular 1080p capable video player or bluray player, it does not need to be 3D capable, but your projector does.
Sorry if this is a little confusing, let me know if you have any other questions.