That's toast, the pinion gear and the bearings are destroyed, that is way too much side movement. Is that a 4WD truck or what? I'd bet it was driven in 4WD for a long while.
I had that happen with the front diff, of my last 98 AWD. If the viscous clutch of an AWD locks up, it's the same as being in 4WD on dry pavement, and the forces will ruin other parts.