No, “normal” in this case means your television device either is widescreen (16:9) or “normal” (4:3) - it has nothing to do with HDMI (you can output via composite, for example, and it still works the same way).
If that didn’t affect your clip you might try looking at your projector settings to see if the option to stretch things to fill the screen is on. Aspect ratio for video is controlled by several things: by the actual resolution of the video as well as the aspect ratio stored in the clip. But it can also be controlled by the output device. Since you’ve adjusted the Live already (to “Normal”) the next step is to adjust your projector (assuming you don’t want to adjust the clip itself, which would be the third thing to try).