Cables are kevlar-reinforced belts and the machine knows how long they are and how much tension in on them so it's relatively easy to compute how much they'd stretch under most conditions.

The frame these belts are mounted on still needs to be stiff, though. A concrete floor is a pretty good option.

The key feature you are missing is that it is a sled that rides on the workpiece, so the cables are just moving it in one plane, while the spindle goes up and down relative to the sled.

So it doesn't need the big, rigid gantry of a traditional machine.

but it also is limited in that you can't cut away too much of the surface of your workpiece, you need to leave enough to keep the sled from falling into the cut.

It's also a lot slower as it's not as rigid.