I suppose an easy way to do it is to have a little drive wheel sticking out about where the license plate is, and as the front wheels turn inward, one of them makes contact with the drive wheel (like the capstan or pinch roller in a reel-to-reel tape machine). But we don't see anything like that in the video.

I think if this is a real thing and not some kind of rigged demo, there's probably something weird about the rear differential or rear drive wheels. Maybe it has an alternate mode where you can't go forward, but the wheels spin in opposite directions when you apply engine torque? I'm not sure what would be the easiest way to do that. Maybe there are two drive shafts, one for forward and one for spinning in place? When the latter of the two is engaged, the "normal" drive shaft is locked in place by a brake forcing the wheels to rotate in equal and opposite directions (due to the differential) and the other drive shaft powers one of the rear wheels somehow.