One of the things that one needs to discuss is how in the heck does one get their vehicle buried up to the axles in the middle of the desert?
We don't know a lot about the situation, but there is a point where one must stop what one's doing and look for another way out.
Of course driving through the biggest mud holes doesn't help either, when he may have been able to simply drive around it.
Sitting in the pickup and spinning the tires as the pickup sinks into the goo doesn't help, and makes recovery much more difficult.
The photo with the pickup shows a bunch of fairly superficial footprints, so the mud doesn't appear to have been that deep The one after the pickup was extracted shows very focal deep pits right around the two left wheels, so likely quite a bit of spinning.
Once there is no forward or backward progress, turn off the engine, get out the winch, or call for help.
Unfortunately there don't appear to be any trees as far as the eye can see. There is a power line, but too far away to be of much help unless one has a mile worth of straps.
A shovel can help reduce the slope in front of the axles, or even around the differentials.
The recovery vehicle apparently tried to make multiple attempts to pull him out, then came up with the idea of the full speed "kinetic" recovery.
