Why are images on retina display pixelated whereas videos are fine?
The videos remain sharp on the retina display because they're scaled down to half their original size (a 720p video is 1280x720, but displayed at 640x360 on YouTube). 

Images on webpages are usually blurry because in order to display at the same physical size as on a non-retina display, they have to be scaled up 2x (unless the website provides 2x source images, like Apple.com does).