Chicken wire is actually a woven wire mesh (aka poultry netting or hexagonal netting.)
The video below shows how chicken wire mesh is woven. You can see how the wires are twisted together to make the hexagonal opening.
A continuous weave makes a difference.
This particular machine is weaving mesh used in making Gabions. Although the mesh is larger (3") and the wires used are heavier (11 gauge and heavier) than the chicken wire you can buy at your local store, the manufacturing process is similar.
There is one difference. This machine is doing continuous weave - the twisted wires run in the same direction the entire length of the twist. Chicken wire available in stores is made with a reverse twist - the twist switches direction (reverses itself) half way through the length of the twist. Continuous weave is inherently stronger than reverse twist. Good to know.
Is this the first time you have seen a loom weaving chicken wire?