Well, seeing that 1080p is, as correctly pointed by chef, 1920*1080 pixels (2073600 pixels) and your friend's laptop has 1280*800 pixels (1024000 pixels) your friends laptop has only half the pixels a 1080p screen would have.
However this has no impact whatsoever in whether you can or can't see a video, the video will resize (losing some quality in the process) to fit the screen's resolution.