Its even more unusual than that. Its got nearly no throw and zero play. The stick doesn't move in the USAF version. A couple of european air forces actually opened up the throw so that the stick will actually move. For a long time serious 'pit builders thought the stick used a pressure sensor for deflection. Turns out that the USAF uses ridiculously strong springs and very sensitive senosrs, so that it only seems like there's no deflection. It gives you a very precise, though slightly unintuitive stick.
There's a few other fighters with side sticks, but not that many. It makes more sense on the side, in my mind. It reduces strain on the right shoulder and lets the pilot rest his arm on something stable for really precise control for things like in-air refueling. He's only having to move from the elbow or wrist, rather than from the shoulder.