8 AWG Used for High Amperage Welding?
The AWG sizes in the table you posted is for electrical installations wires/cables buried in the walls. The wire itself can hold as much current until it melts down, the PVC insultation melts faster than copper, therefore special wires do exist that use silicone instead of PVC.
As for welding machine, the wire is not buried, it stays on floor, no fire hazard is present since the person is always present and trained what to do in case of fire.