SKijoring enthusiasts also call this dryland skijoring, since snow isn't usually involved. It's what them crazy skijoring Alaskans do when there's no snow on the ground, as this story demonstrates.
Amazingly, there's a fairly detailed Wikipedia page about Bikejoring that describes the equipment and the races. There's even a Bikejor blog that's updated on a regular basis.
Photo: "Bikejor II" by Anthony DeLorenzo. CC License.