It looks like someone else got their hands on an Xperia GX in a Japanese DoCoMo store, and decided to take a video showing off the 13MP camera.
Like the still image samples, the video is taken indoors, and does not show much in the way of the full capabilities of the sensor. Nevertheless, it is of full 1080p resolution.
The Sony Xperia GX has garnered some criticism for reportedly being a Japan-only device, despite somehints that an international version may be in the works. Here's to hoping that we'll see the slick device in our neck of the woods someday.