I believe the film taken a Long Branch shows this being done with a flypress of a particular type for the purpose, the barrels being held at close to eye level and inspected by the straightener while still supported in V blocks in the press. The RSAF(E) method at the turn of the last century is reported to have been one of allowing the barrel to fall with the force of solely its own weight onto a hardwood 'anvil' block.
The number of marks on the barrel shown seems excessive; a training piece perhaps?