It's also called a Half-Flip jump. The USFSA accepts landing on either toe, the ISI requires that the skater land on the toe opposite the take-off toe. (The same is true of the Half-Lutz jump, btw) The ISI considers a flip/lutz that lands on the same takeoff toe to be a "1/4" jump, as techskater points out. It is an uncaptured jump, which can be performed at any level in an ISI competition.
In your example, the skater is taking off and landing on the same toe. I use this as a drill before teaching the full flip because the skater lands on the correct foot (albeit, forward-facing) and it keeps the free leg up in front.
It has nothing in common with a Mazurka jump. I was teaching Mazurkas today, what a coincidence!