The machine is a beam saw. Sheet goods are clamped and moved along the table, and stopped for the saw to make cuts. The X axis is probably the sheet movement. The saw carriage should not be any axis.
My guess is that the code outputs other axis for crosscuts. On a typical beam saw, the saw first rips the sheet into multiple strips, Then, each strip is placed back into the saw to make the crosscuts. So, both X and Y cuts on the material are done with one axis on the machine.
The biggest hurdles here is trying to make Mach3 do what it's not designed to do.
A better option imo is to modify the software output to something that works with Mach3, rather than trying to modify Mach3 to work with other software.