Based on the example you showed, you will want to make an animated movie, and simply play the movie back using SFML.
SFML itself doesn't have support for videos. There are third party libs that add support, but the two I tried in the past were buggy - one didn't work, the other I first had to update from SFML 1.x to SFML 2.x (easy enough), and then the video playback would stutter for reasons other than lag, and I didn't have time to debug it.
I just mention this because it's not as easy as "simply play the movie back using SFML". It is absolutely a programming issue.
I still intend to get videos playing in my SFML project eventually, but whenever I do get around to it, it'll probably take me 10 days or so of work.