Hi James,
Not the same camera but with my compact camera the video is downsampled from the native sensor resolution to the video resolution based on the width of the video frame and then if the aspect ratio of the video is different from that of the sensor, the video image is cropped in height. eg 5184×3456 would be downsampled to 1920×1280 and then cropped 100 pixels top and bottom to give 1920×1080. The downsampling ratio is not in general a whole number of pixels (ie a simple binning) so presumably it is done using some kind of interpolation algorithm to maintain image quality.
Cheers
Robin