Adobe Illustrator can export DXF files in a variety of AutoCAD-centric formats. The export provides a variety of options, but it doesn't have anything that would export art in a points-only form.
I've seen other applications offer a choice of Arcs and Lines or Polylines in their DXF export options. The artwork shapes in any DXF file are going to be defined using both anchor points and paths connecting those points. Geometric shapes or open line paths cannot be defined using anchor points alone.
If you're exporting DXF files from Illustrator you'll just have to experiment with both the properties of the artwork as well as export settings (see the attached image of the dialog box). Can the software for your wire EDM cutter import artwork in any other formats, such as EPS?